Question

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

Answer 1

Hi ....
dear..
here is your answer....
....

Answer 2

Solution:-

=> 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..

i.e. 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

i hope it helps you.