Question

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

Answer 1

Step-by-step explanation:

Just put the two zeroes in the above equation if they are zero it will give you 0. If not given roots are not correct.

Answer 2

$let \: \\ p(x) = {8x}^{3} - {4x}^{2} - 18x + 9 \\ p( \frac{1}{2} ) = 8( \frac{1}{2} ) {}^{3} - 4( \frac{1}{2} ) {}^{2} - 18( \frac{1}{2} ) + 9 \\ \: \: \: \: \: \: \: \: \: \: = 8( \frac{1}{8} ) - 4( \frac{1}{4} ) - 18( \frac{1}{2} ) + 9 \\ \: \: \: \: \: \: \: \: \: \: = 1 - 1 - 9 + 9 \\ \: \: \: \: \: \: \: \: \: \: = 0 \\ p( \frac{1}{2} ) = 0 \\ p( \frac{ - 3}{2} ) = 8( \frac{ - 3}{2} ) {}^{3} - 4( \frac{ - 3}{2} ) {}^{2} - 18( \frac{ - 3}{2} ) + 9 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 8( \frac{ - 27}{8} ) - 4( \frac{ - 9}{4} ) - 18( \frac{ - 3}{2} ) + 9 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = - 27 + 9 + 27 + 9 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 18 \\ p( \frac{ - 3}{2} ) \: is \: not \: equal \: to \: zero$

p(1/2) =0 , so 1/2 is a zero of the

given polynomial. But, p(-3/2) is not equal to zero. So, -3/2 is not a zero of the polynomial.

Hope this helps you mate........

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