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If the two zeroes of the polynomial $2 x ⁴ − 3 x ³ − 5 x ² + 9 x − 3$ are $− 3$ and $3,$ then what will be the other two zeroes of the given polynomial?

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12 and − 1

− 1 2 and − 3

12 and 1

72 and − 3

answer is C.

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Detailed Solution

Let the given polynomial is,

p (x) = 2 x ⁴ − 3 x ³ − 5 x ² + 9 x − 3

It is given that

− 3

and

3

are the two zeroes of the above polynomial, therefore we have,

x − 3 x + 3 = x 2 − 3

∴ p x = 2 x ⁴ − 3 x ³ − 5 x ² + 9 x − 3 ⇒ p (x) = 2 x 2 − 3 x + 1 x 2 − 3

Now other two zeroes of

p (x)

can be obtained by equating

2 x 2 − 3 x + 1 = 0.

∴ 2 x 2 − 3 x + 1 = 0

⇒ 2 x 2 − 2 x − x + 1 = 0 ⇒ 2 x − 1 x − 1 = 0 ⇒ x = 12, 1

Therefore the other two zeroes of the given polynomial are

12 and 1 .

Hence option (3) is correct.

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