Question

For what value of k,the polynomial f(x)=
${3x}^{4} - {9x}^{2} + {x}^{2} + 15x + k$
completely divisible by
${3x}^{2} - 5$
​

Answer 1

Step-by-step explanation:

1

Secondary School Math 5 points

If the polynomial f(x) =3x4-9x3+x^2+15x+k is completely divisible by 3x2-5 find the value of k and hence the other two zero of the polynomial

Ask for details Follow Report by Rahul10162 09.03.2018

Answers

rohanharolikar

rohanharolikar Ace

Value of k is -10

zeroes are 1, 2, (-√5/√3), (√5/√3)

4.5

188 votes

THANKS

228

Comments Report

presentmoment

presentmoment Ace

k= -10 is the value of k and the other two zero of the polynomial are 1 and 2.

Given:

f(x)=3 x^{4}-9 x^{3}+x^{2}+15 x+k

To find:

Value of k and other two zero of the polynomial = ?

Solution:

The given polynomial is f(x)=3 x^{4}-9 x^{3}+x^{2}+15 x+k

We need to find the value of k and the other roots ( zeroes) of the polynomial.

Also given that f(x)is divisible by 3 x^{2}-5

when the polynomial is divided by 3 x^{2}-5 the remainder is 0.

Let us divide f(x)with 3 x^{2}-5 is attached below

3 x^{2}-5 and x^{2}-3 x+2 are the roots of the given polynomial.

That is , 3 x^{2}-5=0 \Rightarrow(\sqrt{3 x}-\sqrt{5})(\sqrt{3 x}+\sqrt{5})=0

x=\frac{\sqrt{5}}{\sqrt{3}},-\frac{\sqrt{5}}{\sqrt{3}}

also, x^{2}-3 x+2=0

\begin{array}{l}{x^{2}-2 x-x+2=0} \\ {x(x-2)-1(x-2)=0} \\ {(x-1)(x-2)=0}\end{array}x=1 \text { or } x=2

Therefore, \bold{x=1,2, \frac{\sqrt{5}}{\sqrt{3}},-\frac{\sqrt{5}}{\sqrt{3}}} are the roots of the given polynomial.

Answer 2

Step-by-step explanation:

Hope it will help you

thanks