what are the solutions to the quadratic equation 4x^2 + 34

A quadratic equation solver is a gratis step by pace solver for solving the quadratic equation to notice the values of the variable. With the assist of this solver, nosotros can find the roots of the quadratic equation given by, ax^two + bx + c = 0, where the variable ten has 2 roots. The solution is obtained using the quadratic formula;

where a, b and c are the real numbers and a ≠ 0. If a = 0, and then the equation becomes linear. We tin call information technology a linear equation. The quadratic equation is of 3 types namely,

• Standard form
• Factored form
• Vertex grade

By and large, there are four dissimilar methods to solve the quadratic equation. Those methods are:

• Factoring
• Using square roots
• Completing the squares
• Using quadratic formula

In this, quadratic equation solver folio, we will apply the quadratic formula to solve the quadratic equation.

• Nature Of Roots Quadratic
• Quadratic Equation For Form ten
• Quadratic Equations Class xi

How does the Quadratic Equation Solver Work?

A quadratic equation is nothing but a polynomial of caste 2. The roots of polynomials requite the solution of the equation. Hither nosotros have to solve an equation in the course of ax² + bx + c = 0.

The quadratic equation solver uses the quadratic formula to find the roots of the given quadratic equation. The procedure to use the quadratic equation solver is as follows:

Step 1: Enter the coefficients of the quadratic equation "a", "b" and "c" in the input fields.

Step 2: Now, click the button "Solve the Quadratic Equation" to go the roots.

Step 3: Finally, the discriminant and the roots of the given quadratic equation volition be displayed in the output fields.

Enter the values of a, b and c in the solver given below to solve whatsoever given quadratic equation.

Q u a d r a t i c East q u a t i o n : a 10 ^two + b x + c = 0

Enter the value of a :
Enter the value of b :
Enter the value of c :

Discriminant (D):

x₁ :
x₂ :

where x _one and x ₂ are root one and root two.

If an input is given, it easily shows the solution of the given equation. Use the quadratic solver to check your answers. Use it as a reference when you are finding the unknown values of a variable. When you are numerically solving the quadratic equations, y'all can check information technology with the solver whether your answer is correct or wrong. Once yous find that your answers are right, and then y'all are on the right path to solve the algebraic equations. But, if you lot find that your answers are incorrect, yous should figure out the surface area of mistakes that you had done. The quadratic equation online solver helps to notice out the exact solution of a quadratic equation.

Annotation:

Sometimes, the solutions for the quadratic equation are non rational, and hence, it cannot be obtained using the factoring method. It ways that the unproblematic quadratic equations with rational roots tin exist solved easily with the assistance of the factorization method.

Steps to Solve Quadratic Equation

The input for the quadratic equation solver is of the grade

ax² + bx + c = 0

Where a is non zero, a ≠ 0

If the value of a is zero, then the equation is non a quadratic equation.

The quadratic equation solution is obtained using the quadratic formula:

\(\brainstorm{array}{fifty}x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}\end{array} \)

Normally, nosotros go two solutions, considering of a plus or minus symbol "±". You need to do both the addition and subtraction operation.

The part of an equation " b²-4ac " is called the "discriminant" and it produces the dissimilar types of possible solutions. Some of the possible solutions are

• Instance 1: When a discriminant part is positive, y'all become two existent solutions
• Case 2: When a discriminant part is zero, it gives only one solution
• Instance 3: When a discriminant office is negative, you go complex solutions

Quadratic solver level helps the students of grade 10 to conspicuously know near the different cases involved in the discriminant producing unlike solutions. Here are some of the quadratic equation examples

Quadratic Formula Examples

• Case 1 : b² – 4ac > 0

Example 1: Consider an instance x² – 3x – 10 = 0

Given data : a =i, b = -three and c = -10

bⁱⁱ – 4ac = (-3)²– 4 (1)(-10)

= 9 +forty = 49

b² – 4ac= 49 >0

Therefore, we become two real solutions

The full general quadratic formula is given every bit;

\(\begin{array}{l}ten=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}\end{assortment} \)

\(\begin{array}{l}ten=\frac{-(-3)\pm \sqrt{(-3)^{2}-4(ane)(-10)}}{2(1)}\stop{array} \)

\(\begin{array}{50}x=\frac{3\pm \sqrt{9+40}}{two}\end{assortment} \)

\(\begin{array}{l}x=\frac{three\pm \sqrt{49}}{ii}\end{array} \)

\(\begin{assortment}{l}ten=\frac{iii\pm 7}{2}\stop{array} \)

x= 10/2 , -4/2

x= 5, -2

Therefore, the solutions are 5 and -ii

• Case 2 : b² – 4ac = 0

Case 2: Consider an case 9x² +12x + 4 = 0

Given information : a =ix, b = 12 and c = iv

b² – 4ac = (12)²– 4 (ix)(four)

= 144 – 144= 0

b² – 4ac= 0

Therefore, we get but one distinct solution

The general quadratic formula is given as

\(\begin{array}{l}x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}\finish{array} \)

\(\begin{array}{l}x=\frac{-(12)\pm \sqrt{(12)^{2}-4(9)(four)}}{2(ix)}\end{array} \)

\(\begin{array}{fifty}x=\frac{-12\pm \sqrt{144-144}}{18}\end{array} \)

\(\begin{array}{l}x=\frac{-12\pm \sqrt{0}}{eighteen}\end{array} \)

\(\brainstorm{array}{l}x=\frac{-12}{xviii}\stop{assortment} \)

10= -vi/9 = -two/3

x= -2/3

Therefore, the solution is -two / 3

• Case 3 : b² – 4ac < 0

Example iii: Consider an example x² + 10 + 12= 0

Given data : a =one, b = 1 and c = 12

b² – 4ac = (one)^two– 4 (1)(12)

= 1 – 48 = -47

b² – 4ac= -47 < 0

Therefore, we get complex solutions

The full general quadratic formula is given as

\(\begin{array}{fifty}x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}\end{array} \)

\(\begin{array}{fifty}x=\frac{-(1)\pm \sqrt{(i)^{two}-4(1)(12)}}{2(1)}\end{assortment} \)

\(\begin{assortment}{fifty}x=\frac{-i\pm \sqrt{1-48}}{2}\stop{assortment} \)

\(\begin{assortment}{fifty}x=\frac{-ane\pm \sqrt{-47}}{2}\end{array} \)

\(\begin{array}{l}ten=\frac{-1+i\sqrt{47}}{2}\end{assortment} \)

and

\(\begin{array}{fifty}x=\frac{-1-i\sqrt{47}}{2}\end{array} \)

Therefore, the solutions are

\(\begin{array}{50}x=\frac{-1+i\sqrt{47}}{ii}\end{array} \)

and

\(\begin{array}{50}x=\frac{-1-i\sqrt{47}}{2}\end{array} \)

For more information well-nigh quadratic equations and other related topics in mathematics, register with BYJU'S – The Learning App and picket interactive videos.

Oft Asked Questions on Quadratic Equation Solver

What is meant by the quadratic equation?

In Maths, the quadratic equation is defined every bit an algebraic equation of degree 2, and it should be in the form of ax² + bx + c = 0. Here, a, b, and c are the coefficients of the variable x, and the value of "a" should not be equal to 0. (i.e., a≠ 0). The solutions of the quadratic equation are chosen the roots of the equation.

What are the four different methods to solve the quadratic equation?

The different methods to solve the quadratic equation are:
Factoring
Completing the squares
Using the square root method
Quadratic formula

What is discriminant?

The discriminant D = b² – 4ac reveals the nature of the roots that the equation has. Information technology is determined from the coefficients of the equation.
If D = 0, the roots are equal, real and rational
If D > 0, and likewise a perfect foursquare, the roots are existent, distinct and rational
If D > 0, but not a perfect square, the roots are real, distinct and irrational

What is the standard form of the quadratic equation?

The standard course to correspond the quadratic equation is
Ax² + Bx + C = 0
Here A, B and C are the known values, and A should not be equal to 0.
10 is a variable.

Mention the applications of quadratic equations.

The quadratic equations are used in everyday life activities such as finding the profit of the product, computing the area of the room, athletics, finding the speed of the object, and so on.

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