Question

Find all the zeros of the polynomial x⁴+x³-34x²-4x+120,if two of its zeros are2 and -2

Answer 1

Answer:

The roots are 2, -2, 5 and -6

Step-by-step explanation:

Since 2 and -2 are known to be roots, we know that ( x - 2 ) and ( x + 2 ) are factors.  So

x⁴ + x³ - 34 x² - 4 x + 120 = ( x² + a x + b ) ( x² - 4 )

for some a and b.

Equating constant coefficients:  120 = -4b => b = -30.

Equating coefficients of x³ :  1 = a

So the roots of our quartic are the roots of x² + x - 30 = ( x - 5 ) ( x + 6 ),

and these are 5 and -6.