If one root of equation \(2x^2 - 10x + P = 0\) is 3, then the value of P is

Question

The equation \( (\cos p - 1)x^2 + (\cos p)x + \sin p = 0 \), where \( x \) is a variable with real roots. Then the interval of \( p \) may be any one of the following:

Answer 1

Since 3 is a root, it satisfies the equation: \[ 2(3)^2 - 10(3) + P = 0 \] Simplification yields: \[ 18 - 30 + P = 0 \quad \Rightarrow \quad P = 12 \] Therefore, the answer is \(P = 12\).

If one root of equation \(2x^2 - 10x + P = 0\) is 3, then the value of P is

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The Correct Option is B

Solution and Explanation

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