Question

Find the quadratic polynomial whose zeroes are 3+/2 and 3-√2.

Answer 1

Answer:

x² - 6x + 7

Step-by-step explanation:

Given :-

zeros of the polynomial :-

3 + √2 , 3-√2

To Find :-

The quadratic polynomial.

How To Do :-

Here they given the zeroes of the polynomial. We are asked to find the quadratic polynomial. So first we need to find the value of sum of the zeroes by adding them. Then we need to find the value of product of the zeroes by multiplying them and we need to substitute them in the formula.

Formula Required :-

Quadratic polynomial using zeroes :-

Let,

a , b be the zeros of the polynomial , Then the polynomial is :-

x² -(sum of the zeroes of the polynomial)x + (product of the zeroes of the polynomial)

x² -(a + b)x + (ab)

Solution :-

Sum of the zeroes of the polynomial :-

= 3 + √2 + 3 - √2

= 3 + 3

= 6

Sum of the zeroes of the polynomial = 6.

Product of the zeroes of the polynomial :-

= (3 + √2)(3 - √2)

= (3)² - (√2)²

= 9 - 2

= 7

Product of the zeroes of the polynomial = 7

The required quadratic polynomial is :-

x² - (6)x + (7)

= x² - 6x + 7

The required quadratic polynomial is 'x² - 6x + 7'.