Question

OBTAIN ZEROES OF POLYNOMIAL 2X^4- 5X^3-11X^2+20X+12 IF TWO OF ITS ZEROES ARE 2 AND -2

Answer 1

Heya!!!!

Here's your answer...

Answer 2

SOLUTION:-

Given:

Let f(x)= 2x⁴ - 5x³ - 11x² + 20x +12

⚫(x-2)(x+2) are the zeros of f(x)

Product of zeros:

=) (x-2)(x+2)

=) x(x+2)-2(x+2)

=) x²+ 2x -2x- 4

=) x² - 4

So,

Attachment a division above.

Therefore,

On dividing the f(x) with x² -4, we get;

=) 2x² -5x -3

Now,

=) 2x² -5x -3=0

=) 2x² - 6x + x - 3=0

=) 2x(x- 3) + 1(x-3) =0

=) (x-3)(2x+1)=0

=) x-3=0 or 2x+ 1 =0

=) x= 3 or 2x= -1

=) x= 3 or x= -1/2

Thus,

The other zeros are 3 & -1/2.

Hope it helps ☺️