Question

In a quadratic equation $a{x}^2+bx+c=0$, if $a$ and $c$ are of opposite sign and $b$ is real, then the roots of the equation are

• A. real and distinct
• B. real and equal
• C. imaginary
• D. both roots positive

Answer 1

Answer: (A)

real and distinct

If a and c are of opposite sign, then

$ac<0$

Or

$4ac<0$

Or

$-4ac>0$...(i)

Since $b$ is real.

$b^2\ge 0$ ...(ii)

Hence

From i and ii

$b^2-4ac>0$

Therefore $D>0$.

Hence we get two distinct roots.