Question

Verify if 1/2 and -3/2 are zeroes of the polynomial 8x3 -4x2 -18x+9. If yes, then factorise the polynomial.



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Answer 1

Step-by-step explanation:

The polynomial 2x4−ax3+19x2−20x+122x4−ax3+19x2−20x+12 has the factor in the form (x−k)2(x−k)2, where kk is positive real integer. Find the value of kk and aa and show that the polynomial is non-negative for all real values of xx.

I can't figure out any way to solve this with an unknown factor. Is there any way to do this question? Or the question is missing something?

The answer for this question is k=2,a=10k=2,a=10.

Answer 2

8x3 -4x2 -18x+9

if 1/2 and -3/2 are zeroes of the polynomial 8x3 -4x2 -18x+9. If yes, then factorise the polynomial.

=8(1/2)^3-4(1/2)^2-18(1/2)+9

=8*(1/8)-4*(1/4)-9+9

=1-1+0

=0

hence 1/2 is a root of equation 8x3 -4x2 -18x+9 then satisfy equation

=8(-3/2)^3-4(3-2)^2-17(-3/2)+9

=8*(-27/8)-4*(9/4)-18(-3/2(+9

=-27-9+27+9

=0

hence -3/2 is also a root of equation 8x3 -4x2 -18x+9