Question

Find all the zeros of the polynomial 2x^4-11x^3-16x^2+55x+30 if two of its zeros are √5,-√5.
PLZ ANSWER IF YOU KNOW DONT WASTE TIME OR I WILL REPORT.

Answer 1

Step-by-step explanation:

Let p(x) = 2x⁴-11x³-16x²+55x+30

given that √5 and -√5 are two zeroes of p(x)

(x+√5)(x-√5)

(x)²-(√5)²

x²-5

x²-5)2x⁴-11x³-16x²+55x+30(2x²-11x-6

2x⁴ - 10x²

- +

—————————

-11x³-6x²+55x

-11x³ +55x

+ -

—————————

-6x²+30

-6x²+30

+ -

—————

0

——

now,

2x²-11x-6

2x²-(12-1)x-6

2x²-12x+x-6

2x(x-6) + 1(x-6)

(2x+1)(x-6)=0

2x+1=0 x-6=0

2x=-1 x=6

x= -1/2.

hence, all the zeroes of p(x) are √5,-√5,6 and -1/2