Question

find all the zeroes of p(x) is x³-5x²-2x+24 if the product of zeroes is 12

Answer 1

see the polynomial x³-5x²-2x+24
and 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
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Answer 2

Answer:

Step-by-step explanation:

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