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If one of the zeros of the quadratic polynomial $(k − 2) x 2 − 2 x − (k + 5)$ is 4, find the value of $k$ .

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answer is A.

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Detailed Solution

Given that x = 4 is one of the zeros of the quadratic polynomial

k − 2 x 2 − 2 x − k + 5

.
Zeros of a polynomial can be defined as the points where the polynomial becomes zero.
Let us find the value of k.
Since x = 4 is one of the zeros of the quadratic polynomial. So it will satisfy the given polynomial.
Therefore

(k − 2) (4) 2 − 2 (4) − (k + 5) = 0 ⇒ (k − 2) (16) − 8 − k − 5 = 0 ⇒ 16 k − 32 − k − 13 = 0 ⇒ 15 k − 45 = 0 ⇒ 15 k = 45 ⇒ k = 3

If one of the zeros of the quadratic polynomial

(k − 2) x 2 − 2 x − (k + 5)

is 4, then the value of k is 3.
So, the correct option is 1.

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