Question

Find a quadratic polynomial with zeroes a and b given that a+b=24 and a-b =8. *

Answer 1

Question

Find a quadratic polynomial with zeroes a and b given that a+b=24 and a-b =8.

Solution

Given:-

• a + b = 24 ..........(1)
• a - b = 8 ..............(2)
• a and b are zeroes of polynomial .

Find:-

• Quadratic polynomial

Explanation

We know,

★ a - b = √[(a+b)² - 4.ab]

keep value by equ(1) and equ(2)

➩ 8 = √[(24)²-4.ab]

➩ √[576-4.ab] = 8

Squaring both side,

➩ √[576-4.ab]² = 8²

➩ 576 - 4.ab = 64

➩ 4.ab = 576 - 64

➩ 4.ab = 512

➩ ab = 512/4

➩ ab = 128

For a quadratic polynomial

★ Sum of zeroes (a + b ) = 24

★ product of zeroes ab = 128

Formula of quadratic polynomial

★ x² - (sum of zeroes)x + product of zeroes = 0

➩ x² - 24x + 128 = 0. [ Ans.]

Hence:-

Required Of of polynomial

• x² - 24x + 128 = 0