The sum of the zeros of the polynomial

5x² + (5p – 1)x – (2p + 5) is the same as one fourth of their product. Find the value of p.

Question

Question

This question was previously asked in

NTPC CBT-I (Held On: 9 Jan 2021 Shift 1)

Answer 1

Given:

Sum of the zeros of the polynomial 5x2 + (5p – 1)x – (2p + 5) = 1/4 × Product of zeros

Formulas used:

Standard form of polynomial, ax² + bx + c = 0

Sum of the zeros = - b/a

Product of the zeros = c/a

Calculation:

Sum of the zeros = - (5p - 1)/5

Product of zeros = - (2p + 5)/5

As per the question;

⇒ - (5p - 1)/5 = 1/4 × [- (2p + 5)/5]

⇒ (5p - 1) = (2p + 5)/4

⇒ 20p - 4 = 2p + 5

⇒ 20p - 2p = 5 + 4

⇒ 18p = 9

⇒ p = 9/18 = 1/2

∴ The value of p = 1/2

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