Let a, b be non-zero real numbers. Which of t | vedclass

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Question

(b)

We have,

$\Rightarrow a x^2+(a+b) x+b =0$

$\Rightarrow a x^2+a x+b x+b =0$

$\Rightarrow (a x+b)(x+1) =0$

$\Rightarrow =-\frac{b}{a}

Vedclass · Accepted Answer

$I$ and $III$ only

Vedclass · Answer

(b)

We have,

$\Rightarrow a x^2+(a+b) x+b =0$

$\Rightarrow a x^2+a x+b x+b =0$

$\Rightarrow (a x+b)(x+1) =0$

$\Rightarrow =-\frac{b}{a},-1$

It has at least one negative root, i.e. $-1$. So, it has both roots are real.

$	herefore$ Option $(b)$ is correct.

Let $a, b$ be non-zero real numbers. Which of the following statements about the quadratic equation $a x^2+(a+b) x+b=0$ is necessarily true?

$I$. It has at least one negative root.

$II$. It has at least one positive root.

$III$. Both its roots are real.

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