Math, asked by sudharshini, 1 year ago

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

Answers

Answered by mysticd
16
Given zeroes are α =2, β =-6

i) sum of zeroes = α+β = 2-6 =-4----(1)
ii) product of the zeroes = αβ =2(-6) = -12----(2)

Required quadratic polynomial = x² - (α+β)x+αβ
= x² -(-4)x +(-12)
=x²+4x-12
compare this with ax²+bx+c

a= 1, b= 4 , c= -12

sum of the zeroes = -b/a = - 4/1[ this is equal to (1)]

product of the zeroes = c/a = -12/1 [this is equal to (2)]

sudharshini: Thanku so much....!!
mysticd: u'r welcome
Answered by Anonymous
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.*

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