Question

find the zeros of polynomial f(x) = x^3-5x^2- 2x+24, if it is given that the product of its two zeros is 12

Answer 1

product of the roots =-d/a
such that 12(x)=-24 x=-2
so -2 is one root of f(x)
another two roots are

Answer 2

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.