Polynomials Question - CBSE

Question

If the zeroes of the quadratic polynomial $a x^2 + b x + c$, $c
eq 0$ 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

Accepted Answer

$D = b^2 - 4ac = 0 \Rightarrow 4ac = b^2$. Since $b^2 > 0$ (as $c
eq 0$), $ac > 0$, which means $a$ and $c$ must have the same sign. [1.0 Mark]

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🎯 Official CBSE Marking Scheme:
Deducing $4ac = b^2 > 0 \Rightarrow ac > 0$: 1.0 Mark

Question:

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