Choose the correct answer from the given four options in the following questions:
If the zeroes of the quadratic polynomial $ a x^{2}+b x+c, c
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
Given:
The zeroes of the quadratic polynomial $ax^2+bx+c,\ c\
≠ 0$ are equal.
To do:
We have to find the sign of the roots of the quadratic polynomial.
Solution:
Given that the zeros of the quadratic polynomial $ax^2+bx+c,\ c\
≠ 0$ are equal.
$\Rightarrow$ Value of the discriminant $( D)$ has to be zero for equal roots.
$\Rightarrow b^2-4ac=0$
$\Rightarrow b^2=4ac$
Since $b^2$ cannot be negative, thus, R.H.S. can also be never negative.
Therefore, $a$ and $c$ must have the same sign.
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