Question

Find the zeros of the polynomial 6xcube-7xsquare-11x+12 if x-1 is a facter of polynomial

Answer 1

Solution

let, f(x)=6x³-7x²-11x+12

so now applying the remainder theorem...

x-1=0

=>x=1

now ....

as,if (x-1) is a factor of the polynomial f(x)..then remainder is 0

therefore....

f(1)=6(1)³-7(1)²-11(1)+12

=6-7-11+12

=0

...........,........

now..

6x³-7x²-11x+12

=6x³-6x²-x²+x-12x+12

=(x-1)(6x²-x-12)

=(x-1)(6x²-9x+8x-12)

=(x-1)(3x(2x-3)+4(2x-3))

=(x-1)(2x-3)(3x+4)

therefore the others factors are (2x-3)(3x+4)

therefore the zeroes are

2x-3=0

=>x=3/2

and.

3x+4=0

=>x= -4/3