Find a quadratic polynomial whose zeroes are 2 and -6. verify the relation between the coefficient and zeroes of the polynomial.
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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)]
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....!!
Answered by
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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