Question

Obtain all other zeroes of 3x4+6x3-2x2-10x-5 if two of its zeroes are root 5/3 and -root 5/3

Answer 1

Answer:

Since the two zeroes of the given polynomial p(x)=3x

4

+6x

3

−2x

2

−10x−5 are

3

5

,−

3

5

, therefore,

(x−

3

5

)(x+

3

5

)=x

2

−

3

5

is a factor of the given polynomial.

now, we divide the polynomial p(x)=3x

4

+6x

3

−2x

2

−10x−5 by x

2

−

3

5

as shown below:

8.png

Therefore, 3x

4

+6x

3

−2x

2

−10x−5=(x

2

−

3

5

)(3x

2

+6x+3)

Now, we factorize 3x

2

+6x+3 as follows:

3x

2

+6x+3=0

⇒3(x

2

+2x+1)=0

⇒x

2

+2x+1=0

⇒(x+1)

2

=0(∵(a+b)

2

=a

2

+b

2

+2ab)

⇒(x+1)(x+1)=0

⇒x+1=0,x+1=0

⇒x=−1,x=−1

Hence, the zeroes of the polynomial p(x)=3x

4

+6x

3

−2x

2

−10x−5 are

3

5

,−

3

5

,−1,−1.