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Quadratic Equations
RD Sharma
CBSE
Grade 10

Question:

If $-5$ is a root of the quadratic equation $2x^2 + p x - 15 = 0$ and the quadratic equation $p(x^2 + x) + k = 0$ has equal roots, find the value of $k$.

Step-by-Step Solution

Key Concept: $2(-5)^2 + p(-5) - 15 = 0 \Rightarrow 50 - 5p - 15 = 0 \Rightarrow 5p = 35 \Rightarrow p = 7$. 2nd eq: $7x^2 + 7x + k = 0$. Equal roots $\Rightarrow D = 49 - 28k = 0 \Rightarrow k = 49/28 = 7/4$.
$2(25) - 5p - 15 = 0 \Rightarrow 5p = 35 \Rightarrow p = 7$. [1.0 Mark]
$7x^2 + 7x + k = 0 \Rightarrow D = 49 - 28k = 0 \Rightarrow k = 49/28 = 7/4$. [1.0 Mark]

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🎯 Official CBSE Marking Scheme:
Solving $p = 7$: 1.0 Mark
Solving $k = 7/4$: 1.0 Mark

Correct Answer:
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