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Is the given statement true or false?

1 and -3 the zeroes of the polynomial $p (x) = 2 x 2 + 5 x − 3.$

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True

False

answer is B.

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Detailed Solution

The given polynomial is

p (x) = 2 x 2 + 5 x − 3.

We know that the zero of polynomials is the value of

x

at which

p x = 0.

To find the value of

x

in the above equation, we solve the equation

p x = 0

by mid-term splitting.

⇒ p (x) = 2 x 2 + 5 x − 3 = 0 ⇒ 2 x 2 + 5 x − 3 = 0 ⇒ 2 x 2 + 6 x − x − 3 = 0 ⇒ 2 x (x + 3) − 1 (x + 3) = 0 ⇒ (2 x − 1) (x + 3) = 0

Now, either

2 x − 1 = 0

x + 3 = 0

Therefore, either

x = 12 or x = − 3.

Thus,

12

and -3 are the zeroes of the given polynomial.
Hence, the given statement is false, and so option (2) is correct.

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