Question

write a quadratic polynomial whose zeroes are 2,-6 verify the relation between the coefficient and zeroes of the polynomial

Answer 1

here is your answer by Sujeet,
we know that,

Let to be alpha and beta are the zero of polynomial

a+b=2-6=-4
ab=2*-6=-12
then,

we know that
ax²-(a+b)x+ab
x²-(-4)x+(-12)
x²+4x-12
then,

Splitting middle term,

x²+4x-12
x²+6x-2x-12
x(x+6)-2(x+6)
(x-2)(x+6)


x-2=0
x=2

x+6=0
x=-6

verified


that's all

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.*