Question

If the zeroes of the quadratic polynomial $x^2+bx+c,c\ne 0$ are equal, then:

• A. c and a have the same sign
• B. c and b have opposite signs
• C. c and a have opposite signs

Answer 1

The correct option is A c and a have the same sign

For equal roots
$b^2-4ac=0$
$\Rightarrow b^2=4ac$
$\Rightarrow ac=\frac{b^2}{4}$
$\Rightarrow ac>0$ (Since square of any number cannot be negative)
Which is only possible when a and c have same sign.