Question

find the quadratic polynomial whose zeroes are 2 and -6 verify the relation between cofficients and zero of polynomial

Answer 1

x² + 4x - 12 is the quadratic eq. whose zeroes are 2 and -6 

α + β = -b/a
2 +(-6) = -(4)/1
-4 = -4

αβ = c/a
2×(-6) = -12/1
-12 = -12

Answer 2

Quadratic polynomial = x²-(sum of zeros)x + product of the zeros.

Given, zeros are 2 and -6.

Sum of the zeros = 2+(-6) = 2-6 = -4
product of the zeros = 2(-6) = -12

Quadratic polynomial = x² - (-4)x+ (-12)
= x² + 4x - 12.

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Relationship between coefficients and zeros if the polynomial :-

Sum of the zeros = -4 = -(-4)/1 = -b/a

Product of the zeros = -12 = c/a.

:)