Question

7. Find all zeroes of polynomial x^-3x²-x² + 9x-6, of two of its zeroes are √3and -√3
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Answer 1

Answer:

Solution:

Let p(x)=4x

4

−20x

3

+23x

2

+5x−6

If two of its zeroes are 2 and 3.

So, p(x)=4x

4

−20x

3

+23x

2

+5x−6

⇒p(x)=(x−2)(x−3)(4x

2

−1)

⇒p(x)=(x−2)(x−3)(2x−1)(2x+1)

For zeroes of polynomial, p(x)=0

(x−2)=0 or (x−3)=0 or (2x−1) or (2x+1)=0

x=2 or x=3 or x=

2

1

or x=

2

−1

Hence, all zeroes of the polynomial are 2,3,

2

1

and

2

−1

.