Question

obtain all other zeroes of the polynomials 4x4+x3-72x2-18x.if two of its zeros are 3 root 2 and -3 root 2

Answer 1

→ refer to the attachment for YOUR ANSWER

Answer 2

Answer:

The other roots of the given function are 0 and -0.25.

Step-by-step explanation:

The given polynomial is

$P(x)=4x^4+x^3-72x^2-18x$

It is given that $3\sqrt{2}$ and $-3\sqrt{2}$ are roots of the given polynomial. So, $(x-3\sqrt{2})$ and $(x+3\sqrt{2})$ are factors of the given polynomial.

$(x-3\sqrt{2})(x+3\sqrt{2})=x^2-18$

Using long division method, divide the given polynomial by $x^2-18$.

The quotient is $4x^2+x$.

The factor form of the given polynomial is

$P(x)=4x^4+x^3-72x^2-18x=(x-3\sqrt{2})(x+3\sqrt{2})(4x^2+x)$

$P(x)=4x^4+x^3-72x^2-18x=(x-3\sqrt{2})(x+3\sqrt{2})(4x+1)x$

To find the roots equate each factor equal to 0.

$x=3\sqrt{2},-3\sqrt{2},0.25,0$

Therefore the other roots of the given function are 0 and -0.25.