Question

If the roots of the quadratic equation, ax² + bx + c = 0, a ≠ 0 are real and equal, then each root is equal to:

Options

• `(-a)/(2b)`

• `(-b)/(2a)`

• `(-2a)/(b)`

• `(-c)/(2a)`

Answer 1

`bb((-b)/(2a))`

Explanation:

Let us consider the quadratic equation ax² + bx + c = 0, a ≠ 0 and a, b, c are real numbers.

Let r₁ and r₂ be the roots of this equation.

`r_1 = (-b + sqrt(D))/(2a)`

`r_2 = (-b - sqrt(D))/(2a)`

If the roots are real and equal then D = 0,

`r_1 = (-b + sqrt(0))/(2a)`

`r_1 = (-b)/(2a)`

`r_2 = (-b - sqrt(0))/(2a)`

`r_2 = (-b)/(2a)`

`r_1 = r_2 = (-b)/(2a)`

Hence, each root can be given by `(-b)/(2a)`.