Question

find the quadratic polynomial having zero a+b , a- b.

Answer 1

first we need to find the sum and product of zeros
sum= a+b+a-b
=2a
product=(a+b)×(a-b)
=a square -ab +ab -b square
=a square - b square
now p(x)=k{x square -(sum of Zeros ) X + (product of Zeros )}
p(x)=k{x square -(2a)x +(a square - b square)}
p(x)=k{x square -2ax + a square - b square}

Answer 2

★ QUADRATIC RESOLUTION ★

Quadratic polynomial having roots as ( a + b ) , ( a - b ) :

x² - [ a + b + a - b ] x + a + b ( a - b )

General standard quadratic equation format :

x² - [ sum of roots ] x + product of roots

Here , Sum of the two roots : a + b + a - b = 2a

product of respective roots : a-b ( a + b ) = a²-b²

Now framing the equation -

x² - 2ax + (a²-b²)

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