Question

the sum of two zeros of a quadratic polynomial is 6. if one of the zeroes is 3-√7 what is the polynomial?

Answer 1

hope it helps

please follow me ☺️

Answer 2

Answer:

x² - 6x + 2

Step-by-step explanation:

Assume that α and β are the zeroes of a quadratic polynomial.

Given that one of the zero is 3 - √7 say (α).

Sum of its zeroes = (α+ β) = 6

(α+ β)= 6

(3 - √7) + β= 6

β = 6- (3 - √7)

β = 6 - 3 + √7

β= 3 + √7

Product of zeroes (αβ) = (3 + √7)(3 - √7)

αβ = (3)² - (√7)²

αβ = 9 - 7

αβ = 2

Polynomial= k × [x² - (Sum of zeroes)x +(Product of zeroes)]

= k[ x² - (α + β)x +(αβ)]

Where, k = 1

= x² - (6)x + (2)

= x² - 6x + 2

Hence, the polynomial is x² - 6x + 2.