Question

Question 3: If sum of the roots of a quadratic equation is − 7 and product of the roots is 12. Find the quadratic equation

Answer 1

Step-by-step explanation:

let the roots be a,b

then quadratic equation =x^2-(a+b)+ab

so,the answer for question =x^2-(-7)+12

=x^2+7x+12

hope it helps

mark as the brainliest answer

Answer 2

★ ${\underline{\underline{\large{\bold{\pink{Answer}}}}}}$

${x}^{2} + 7x + 12 = 0$

Given :

In a quadratic equation,

• sum of roots is − 7.
• product of the roots is 12.

To Find :

• The quadratic equation.

$\boxed{\red{Solution:-}}$

➸ Let the roots be $\alpha$ and $\beta$.

➸ We know that, if the sum and product of roots are given then the quadratic equation would be,

${x}^{2} - ( \alpha + \beta )x + \alpha \beta = 0$

➸ As given,

$\alpha + \beta = - 7 \\ \\ and \: \: \: \alpha \beta = 12$

➸ So, putting the values we get,

${x}^{2} - ( \alpha + \beta )x + \alpha \beta = 0 \\ \\ = > {x}^{2} - ( - 7)x + 12 = 0 \\ \\ = > {x}^{2} + 7x + 12 = 0$

$\therefore$ The equation is

${x}^{2} + 7x + 12 = 0$

Verification :

${x}^{2} + 7x + 12 = 0 \\ \\ = > {x}^{2} + (4 + 3)x + 4 \times 3 = 0 \\ \\ = > {x}^{2} + 4x + 3x + 12 = 0 \\ \\ = > x(x + 4) + 3(x + 4) = 0 \\ \\ = > (x + 4)(x + 3) = 0 \\ \\ = > (x + 4) = 0 \\ \\ = > x = - 4 \\ \\ = > (x + 3) = 0 \\ \\ = > x = - 3$

➸The roots are - 4 and - 3.

➸The sum of the roots is (- 4) + (- 3) = - 7

➸The products of the roots is (- 4) × (- 3) = 12

Hence, Verified.