Question

If the zeros of the quadratic polynomial ax2+bx+c are equal then

Answer 1

Step-by-step explanation:

the value of b^2-4ac is zero

Answer 2

The zeros of the quadratic polynomial, then $b^2=4ac$.

Step-by-step explanation:

The given quadratic polynomial is:  $ax^2+bx+c$

Let the equal zeros = α and α

We know that,

The sum of zeros,

α + α = $\dfrac{-b}{a}$

⇒ 2α =$\dfrac{-b}{a}$

⇒ α = $\dfrac{-b}{2a}$       ......... (1)

The product of zeros,

αα = $\dfrac{c}{a}$

⇒ $\alpha^2=\dfrac{c}{a}$

From equation (1), we get

⇒ $(\dfrac{-b}{2a})^2=\dfrac{c}{a}$

⇒ $\dfrac{b^2}{2a^2}=\dfrac{c}{a}$

⇒ $b^2=4ac$

Thus, the zeros of the quadratic polynomial, then $b^2=4ac$.