Quadratic Equations
RD Sharma
CBSE
Grade 10
Question:
If the roots of $a x^2 + b x + c = 0$ are equal in magnitude but opposite in sign, then:
(a) $b = 0$
(b) $c = 0$
(c) $a = 0$
(d) $b = c$
Step-by-Step Solution
Key Concept: Roots $\alpha, -\alpha \Rightarrow \text{sum} = 0 \Rightarrow -b/a = 0 \Rightarrow b = 0$.
Sum of roots $= \alpha + (-\alpha) = 0 \Rightarrow -b/a = 0 \Rightarrow b = 0$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Deducing $b = 0$: 1.0 Mark
Correct Answer: $b = 0$
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