Question

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

(a) c and a have opposite signs (b) c and b have opposite signs

(c) c and a have the same sign (d) c and b have the same sign

Answer 1

Let the given quadratic polynomial be f(x) = $a{x}^2+bx+c$.
Suppose $\alpha$ and $\beta$ be the zeroes of the given polynomial.
Since $\alpha$ and $\beta$ are equal so they will have the same sign i.e. either both are positive or both are negative.
So, $\alpha \beta >0$
But, $\alpha \beta =\frac{c}{a}$
∴ $\frac{c}{a}>0$, which is possible only when both have same sign
Hence, the correct answer is option C.