alpha,beta and gamma are zeroes of polynomial f (x)=x^3-5x^2-2x+24.If it is given that the product of two of its zeroes is 12.Find the zeroes of the polynomial.
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just used some properties that were basic that u must ve knowing and I have tried my best in explanation hope u understand
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Hi mate,
solution: x³-5x²-2x+24
compare with ax³+bx²+cx+d
α+β+y=-b/a
=5
αβy=-d/a
=-24
12y= -24
(as given the product of two. zeros ie αβ=12)
y= -2.
α+β+y=5
α+β-2=5
α+β =7. .................(1)
(α+β)²=7²
(α-β)²+4αβ=49
(α-β)²+4*12=49
(α-β)²+48= 49
(α-β)² =1
α-β = √1
α-β=1. ....................(2)
subtracting (2) From (1)
α+β-(α-β)=7-1
α+β-α+β=6
2β =6
β=3
putting the value of β in the (2) eq
α-3=1
α=4
α=4,β=3,y=-2
product of α and β = 4 * 3 = 12
I hope it helps you.
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