Question

The equation $(a{x}^2+bx+c)(-a{x}^2+dx+c)$ = 0 ; ac $\ne$ 0 , has

• A. Exactly four real zeroes
• B. At least two real zeroes
• C. At most two real zeroes
• D. No real zeroes

Answer 1

The correct option is B

At least two real zeroes

Let $D_1$ and $D_2$ be the discriminants of

$a{x}^2+bx+c=0$ and $-a{x}^2+dx+c$ , respectively. Then,

D = $b^2$ - 4ac and $D_2$ = $d^2+4ac$ .

Now, $D_1$ + $D_2$ = $b^2+d^2$ $>$ 0

$\Rightarrow$ At least one of the equations $a{x}^2+bx+c=0$

Hence, at least one of the equations $a{x}^2+bx+c=0$

And $-a{x}^2+dx+c=0$ has real roots. Thus the given polynomial has at least two real roots.