Question

If 2 and -2 are the zeros of the polynomial x⁴+x³-34x²-4x+120. Find all zeros of the polynomial?

Answer 1

p(x)=x^3-34x^2–4x+120
p(2)=2^3–34(2)^2–4(2) + 120
=8– 34×4–8 + 120
=–136+120
=–16...... [2 is not polynomial zero]

p(–2)=–2^2 – 34×4 +8 +120
=8-136+128
=136-136
=0........{-2 is the zero of polynomial]}
thanks

Answer 2

x=2 & x= -2

are the zeroes of p(x)

( using identity ( a - b ) ( a +b ) = a² - b²

then,

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

x²- 4=0.......(i)

When we divide p ( x ) by ( i ) we get the other zeros

x⁴+x³-34x²-4x+120/x²- 4

We get , x²+x-30=0

. x²+(6-5)x-30=0

(x+6)(x-5)=0

x=-6 & x=5 zeroes of the x⁴+x³-34x²-4x+120