Question

If 3 and -3 are two zeroes of polynomial p(x)=x⁴+x³-11x²-9x+18 then find remaining two zeroes.​

Answer 1

Answer:

The given polynomial equation is

$x^{4}+x^{3}-11x^{2} -9x+18=0$

Also,since  -3 & 3 are already the roots of the given equation let the other two remaining roots be α &β.

So, ther sum of roots  that is;

+3 - 3 +α +β = -1

that is,

α+β=  -1,

and, the product of the roots is 18.

∴ (α)(β)(3)(-3)=18

Ξ αβ=-2

Ξ β=-2/α

So, putting this value of β in already obtained equation.

α-2/α = -1

or,

α² + α -2 =0

∴ (α+2)(α-1)=0

or,

α=-2 and β=-2/-2 = 1

and,

for

α=1 β=-2.

Howevre, the value of the roots α & β are absolutely ambiguous i.e the solution set remains the same.

∴ The remaining two roots of the given equation are -2 & +1.

Hope this helps you !!