Question

find the quadratic polynomial whose zeroes are a+b and a-b where a,b are real numbers

Answer 1

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Answer 2

Given,

• The zeroes of the polynomial are a+b and a-b.

To find,

• We have to find the quadratic polynomial whose zeroes are a+b and a-b.

Solution,

The quadratic polynomial whose zeroes are a+b and a-b where a,b are real numbers is  $x^2 -2ax + (a^2-b^2)$.

We can simply find the quadratic polynomial by using the formula,

       $x^2 -(sum of zeroes)x +(product of zeroes)$      (1)

Sum of zeroes = a+b+a-b

                        = 2a

Product of zeroes = (a+b)(a-b)

Using (a+b)(a-b) = a²-b²

                              = (a²-b²)

Substituting the value of the sum of zeroes and product of zeroes in (1), we get

                        $x^2 -2ax + (a^2-b^2)$

Hence, the quadratic polynomial whose zeroes are a+b and a-b where a,b are real numbers is  $x^2 -2ax + (a^2-b^2)$.