Question

Obtain all other zeroes of the polynomial 4x 4 +x 3 -72x 2 -18x,if two of its zeroes are 3 root 2 and -3 root 2

Answer 1

hope it helps.........

Answer 2

Answer:

The other two zeroes are x=0 and $x=\frac{-1}{4}$

Step-by-step explanation:

$\text{Given the two zeroes of polynomial }4x^4 +x^3 -72x^2 -18x \text{ are }3\sqrt2 \text{ and } -3\sqrt2$

we have to find the other two zeroes of the above polynomial.

As $3\sqrt2$ and $-3\sqrt2$ are two zeroes implies if we divide the polynomial by two factors remainder will be zero.

$(x-3\sqrt2)(x+3\sqrt2)$ is the factor of of the polynomial $4x^4 +x^3 -72x^2 -18x$.

By dividing we get the quotient which is

$(4x^2+x)$

⇒ $x(4x+1)$

In order to find the other two zeroes put the quotient equals to zero, we get

$x(4x+1)=0$

⇒ x=0 and $x=\frac{-1}{4}$

Hence, the other two zeroes are x=0 and $x=\frac{-1}{4}$