Question

Obtain all other zeroes of x4 + 5x3 - 2x2 - 40x -48 if two of its zeroes are 2√2 and -2√2.

Answer 1

zeroes are 2√2 and -2√2
factors are (x-2√2)(x+2√2)
=x²-(2√2)²
=x²-8
now we divide the p(x) from x²-8
x4+5x³-2x²-40x-48/x²-8
remainder comes out x²+5x+6
you can check out in the attachment how remainder comes
now we split the remainder
x²+5x+6=x²+2x+3x+6
=x(x+2)+3(x+2)
=(x+3)+(x+2)
x=-3 and x=-2
all the zeroes are 2√2,-2√2,-3and-2

Answer 2

Answer:

zeroes are 2√2 and -2√2

factors are (x-2√2)(x+2√2)

=x²-(2√2)²

=x²-8

now we divide the p(x) from x²-8

x4+5x³-2x²-40x-48/x²-8

remainder comes out x²+5x+6

you can check out in the attachment how remainder comes

now we split the remainder

x²+5x+6=x²+2x+3x+6

=x(x+2)+3(x+2)

=(x+3)+(x+2)

x=-3 and x=-2

all the zeroes are 2√2,-2√2,-3and-2