Question

find the quadratic polynomial whose zeros are 2 and -6 . verify the relationship between the coefficient and the zeros of the polynomial

Answer 1

Sum of zeroes =2+(-6)
=2-6
=-4
Product of zeroes =2×(-6)
=-12
Quadratic polynomial =
x^2-(sum of zeroes)x+product of zeroes
=x^2-(-4)x+(-12)
=x^2+4x-12

Answer 2

AnsWer:-

↝α+β=2+(-6)

↝α+β=-4

↝αβ=2×-6

↝αβ=-12

✪Using the Formula

→k[x²-(α+β)x+αβ]

↝k[x²-(-4)x+(-12)]

↝k[x²+4x-12]

•Let k=1•

↝1[x²+4x-12]

☞x²+4x-12 is the Polynomial.

*Since The Zeros Form a Polynomial,It Verifies the Relation b/w coefficients and the zeros of the polynomial.*