Question

Find all zeros of the polynomial x⁴+x³-9x²-3x+18 if two of its zero are -√3 and √3

Answer 1

-3 and 2 are the remaining roots

Answer 2

Answer:Let p(x)=x⁴+x³-9x²-3x+18

Step-by-step explanation:-√3 and √3 are the two zeroes then (x+√3)(x-√3)=x²-(√3)²=x²-3 is factor of p(x)

Divide x⁴+x³-9x²-3x-18 by x²-3

=x²+x-6

Now,

Divident=Divisor×Quotient+Remainder

P(x)=(x²-3)×(x²+x-6)+0

=(x²-3)×{x²+(3-2)x-6}

=(x²-3)×(x²+3x-2x-6)

=(x²-3)×{x(x+3)-2(x+3)}

=(x²-3)×(x+3)(x-2)

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

Either x+3=0. x-2=0

x=-3. x=2

Therefore,all the zeroes of the polynomial p(x) are-√3,√3,-3 and2