Question

obtain all zeroes of the polynomial p(x)=2x4-2x3-7x2+3x+6 if its two zeroes are root 3/2 and-root3/2​

Answer 1

SOLUTION:-

Given:

p(x)=2x⁴ -2x³ -7x² +3x +6 if it's two zeroes are root 3/2 & -root 3/2.

To find:

All the zeroes of the polynomial.

Explanation:

We have,

$Two \: zeroes = \sqrt{ \frac{3}{2} } \: \: \: \: and \: \: \: \: - \sqrt{ \frac{3}{2} }$

Therefore,

Two factor of the p(x)

$(x + \sqrt{\frac{3}{2} } )(x - \sqrt{ \frac{3}{2} } )$

Multiplying the two factors we get;

$( {x}^{2} - \sqrt{ \frac{3}{2} } x + \sqrt{ \frac{3}{2} } x - \frac{3}{2} ) \\ \\ ( {x}^{2} - \frac{3}{2} )$

Therefore,

(x² -3/2) divided by p(x)2x⁴-2x³-7x²+3x+6

Above the attachment a division.

&

=) 2x² -2x -4 = 0

=) x² - x -2 =0

=) x² - 2x +x -2=0

=) x(x-2) + 1(x-2) =0

=) (x-2) (x+1) =0

=) x-2 = 0 or x+1 =0

=) x= 2 or x= -1.

Answer 2

Hope this will help you

Plzzz..... mark my answer as 'Brainliest '