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If one of the zeroes of the quadratic polynomial $2 x 2 − 3 x + p$ is $3$ , find its other zero. Also find the value of $p$ .

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p = − 5

and zero

= 4

p = 5

and zero

= − 4

p = 9

and zero

= − 12

p = − 9

and zero

= − 32

answer is A.

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Detailed Solution

Given polynomial

2 x 2 − 3 x + p

has one of its zeroes as

3

. We need to find the other zero and the value of

p

.
Zeroes of the polynomial are those where

p (x) = 0

.
Let us assume

p (x) =

2 x 2 − 3 x + p

It is given that

3

is the zero of the polynomial

2 x 2 − 3 x + p

, therefore, we have,

p (3) = 0 ⇒ 232 − 3 (3) + p = 0

⇒ 18 − 9 + p = 0 ∴ p = − 9

Now the given polynomial is,

2 x 2 − 3 x − 9 = 0

Factorizing the polynomial

2 x 2 − 3 x − 9 = 0,

we have,

2 x 2 − 3 x − 9 = 0 ⇒ 2 x 2 − 6 x + 3 x − 9 = 0 ⇒ 2 x + 3 x − 3 = 0 ∴ x = 3, − 32

Hence the other zero of the polynomial

2 x 2 − 3 x − 9 = 0,

− 32

and the value of

p = − 9.

Therefore, option 1 is correct.

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If one of the zeroes of the quadratic polynomial 2 x 2 −3x+p is 3 , find its other zero. Also find the value of p .

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If one of the zeroes of the quadratic polynomial $2 x 2 − 3 x + p$ is $3$ , find its other zero. Also find the value of $p$ .