Question

# What are the solutions of the quadratic equation ?

- x = -1 and x = 3
- x = 1 and x = -3
- x = 1 and x = 3

Hint:

**Hint:- **

The word "quadratic" is originated from the word "quad" and its meaning is "square". It means the quadratic equation has a variable raised to 2 as the greatest power term. The standard form of a quadratic equation is given by the equation ax^{2} + bx + c = 0, where a ≠ 0. We know that any value(s) of x that satisfies the equation is known as a solution (or) root of the equation and the process of finding the values of x which satisfies the equation ax^{2} + bx + c = 0 is known as solving quadratic equations.

## The correct answer is: x = -1 and x = 3

- The given equation is 4x
^{2}-8x-12=0.
- We can see 4 is the like factor of all terms in the equation . So we can write the equation as

4 (x^{2}- 2x - 3 )= 0

Factoring x^{2} - 2x - 3

The first term is, x^{2} its coefficient is 1 .

The middle term is, -2x its coefficient is -2 .

The last term i.e. constant is -3

Step-1 : Multiply the coefficient of the first term by the constant 1 × (-3) = -3

Step-2 : Find two factors of -3 whose sum equals the coefficient of the middle term, which is -2 .

-3 + 1 = -2

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -3 and 1

x^{2} - 3x + 1x - 3

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (x-3)

Add up the last 2 terms, pulling out common factors :

1 • (x-3)

Step-5 : Add up the four terms of step 4 :

(x+1) • (x-3)

Which is the desired factorization

- So, the equation becomes

4 (x + 1) (x - 3) = 0

- A product of several terms equals zero. When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately . In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solve : 4 = 0

This equation has no solution.

A a non-zero constant never equals zero.

Solve : x+1 = 0

Subtract 1 from both sides of the equation :

x = -1

Solve : x - 3 = 0

Add 3 to both sides of the equation :

x = 3

- Therefore, we get the roots of the equation as x = -1 and x = 3.

Note:-There are different ways of solving quadratic equations.

- Solving quadratic equations by factoring
- Solving quadratic equations by completing the square
- Solving quadratic equations by graphing
- Solving quadratic equations by quadratic formula

But most popular method is solving quadratic equations by factoring.

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As opposed to this, a circle's area indicates the space it occupies.

The circle circumference is the length when we cut it, open and draw a straight line from it.

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where,

R is the circle's radius.

π is a mathematical constant with an estimated value of 3.14 (to the nearest two decimal places).