Question

If a B are the two zeroes of the polynomial 25p2 -15p + 2, find a quadratic polynomial whose zeroes are 1/2a and 1/2b
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Answer 1

Answer:

Step-by-step explanation:

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By - Janvi.....

Hello,

P(X) => 25P²-15P+2

Here,

A = 25 , B = -15 and C = 2

Sum of zeroes = -B/A

Alpah + Beta = -(-15)/25

Alpha + Beta = 15/25

And,

Product of zeroes = C/A

Alpha × Beta = 2/25

Sum of Zeroes of Quadratic polynomial whose zeroes are 1/2 ×Alpha and 1/2Beta

Sum of zeroes = 1/2Alpha + 1/2Beta

=> 1/2 × (Alpha + Beta)/(Alpha × Beta)

=> 1/2 × (15/25)/(2/25) = 1/2 × 15/2 = 15/4

And,

Product of zeroes = 1/ 2 Alpha × 1/2 beta = 1/4 Alpna × Beta = 1/ 4 × 2/25

=> 25/8

Therefore,

Required Quadratic polynomial = X²-(Alpha + Beta)X + Alpha × Beta

=> X² - 15/4 X + 25/8

=> X²-15X/4 + 25/8

=> 8X²-30P+25