Question

The constant term of ax2+bx+c=0 is zero, then the sum and product of roots are

Answer 1

Sum = α + β = -b/a

Product = αβ = c/a

Answer 2

If the constant term of $ax^{2}+bx+c=0$ is zero, then the sum and the product of the roots are $(-\dfrac{b}{a})$ and $0$ respectively.

Concept to be used:

If $\alpha$ and $\beta$ be the roots of the equation $ax^{2}+bx+c=0$, then

sum of the roots $(\alpha+\beta)$ is $(-\dfrac{b}{a})$

product of the roots $(\alpha\beta)$ is $\dfrac{c}{a}$

Step-by-step explanation:

Given that, the constant term of the equation $ax^{2}+bx+c=0$ is zero. This means:

• $c=0$

Now, sum of the roots is

$-\dfrac{b}{a}$

and the product of the roots is

$\dfrac{c}{a}=\dfrac{0}{a}=0$

• since $c=0$

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