Question

Ifa and B are the zeros of the quadratic polynomial 2x2-5x+7, then find the quadratic polynomial
whose zeros are ( 3a+4B) and (4a+3B).

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Answer 1

Answer: Required quadratic polynomial is 2x² - 25x + 82

Step-by-step explanation:

Given that A and B are the zeros of the polynomial 2x² - 5x + 7

Note

Sum of Zeros : - x coefficient/x² coefficient

Product of Zeros : constant term/x² coefficient

Here,

Sum of Zeros :

A + B = -(-5)/2

→ A + B = 5/2

Product of Zeros :

AB = 7/2

Let S and P be the sum and product of zeros of required polynomial

Sum of Zeros

S = (2A + 3B) + (3A + 2B)

→ S = 5(A + B)

→ S = 5(5/2)

→ S = 25/2

Product of Zeros

P = (2A + 3B)(3A + 2B)

→ P = 6A² + 4AB + 9AB + 6B²

→ P = 6A² + 13AB + 6B²

→ P = (6A² + 12AB + 6B²) + AB

→ P = 6(A + B)² + AB

→ P = 6(5/2)² + 7/2

→ P = 150/4 + 7/2

→ P = 75/2 + 7/2

→ P = 82/2

Required Polynomial

x² - Sx + P

= x² - (25/2)x +82/2

= 2x² - 25x + 82

Thus,the required quadratic polynomial is 2x² - 25x + 82