Question

if the zeros of polynomial x³-6x²-8x+24 is in the form of a-b , a and a+b then find all zeros can anybody answer this question​

Answer 1

Answer:

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Answer 2

Question :

If the zeroes of the polynomial x³-6x²-8x+24 is in the form of α-β , α , α+β then find all zeroes

Solution :

We are given a cubic polynomial x³-6x²-8x+24 and roots/zeroes of the poly. is α-β , α , α+β

Compare given cubic poly. with ax³+bx²+cx+d ,

a = 1 , b = -6 , c = -8 , d = 24

Sum of zeroes of the poly. is ,

$\implies \sf{(\alpha -\beta)+\alpha+(\alpha+\beta)=-\dfrac{b}{a}}$

$\implies \sf 3\alpha=-\dfrac{(-6)}{1}$

$⟹α= 2$

Product of zeroes of the poly. is ,

$:\implies \sf (\alpha-\beta)(\alpha)(\alpha+\beta)=-\dfrac{d}{a}$

( a + b ) ( a - b ) = a² - b²

α = 2

$:\implies \sf 2(\alpha^2-\beta^2)=-\dfrac{24}{1}$

$:\implies \sf ((2)^2-\beta^2)=-12$

$:\implies \sf \beta^2=16$

$:⟹β=± 4$

So , Zeroes of the polynomial are as follows ,

(α-β) = (2-4) = -2 or (α-β) = (2-(-4)) = 6

α = 2

(α+β) = (2+4) = 6 or (α+β) = (2+(-4)) = -2

-2 , 2 , 6 are zeroes of the polynomial

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