Question

if alpha and beta are the zeros of the polynomial 25 x 2-15x+2 find a quadratic polynomial whose zeroes are 1/alpha and 1/beta.ASAP with steps

Answer 1

Step-by-step explanation:

refer o the attachment .

Answer 2

Answer:

$\sf 8x^2- 30x + 25$

Step-by-step explanation:

Given Problem:

if alpha and beta are the zeros of the polynomial 25 x 2-15x+2 find a quadratic polynomial whose zeroes are 1/alpha and 1/beta.

Solution:

To Find:

A quadratic polynomial whose zeroes are 1/alpha and 1/beta.

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Method:

P(X) => 25x²-15x (2)

Here,

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

Sum of zeroes = -B/A

Alpha+ 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

=> 8X²-30x+25