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If one of the zeroes of the quadratic polynomial $2 x^{2} + px + 4$ is 2, find the other zero. Also find the value of p.

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p = - 6, other zero = 1

p = - 7, other zero = 1

p = - 1, other zero = 1

p = - 2, other zero = 1

answer is C.

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Detailed Solution

Given, one of the zeroes of the quadratic polynomial

2 x^{2} + px + 4

is 2.
We need to find the other zero and the value of p.
Using the formula, product of the zeroes

= \frac{c}{a}

.
Let the other root be a.
Therefore,

2 \times a = \frac{4}{2}

\Rightarrow a = 1

Therefore, the other zero is 1.
Also, the sum of the zeroes

= - \frac{b}{a}

\Rightarrow 1 + 2 = - \frac{p}{2}

\Rightarrow 3 \times 2 = - p

\Rightarrow p = - 6

Therefore,

p = - 6 and other zero = 1 .

Hence, the correct option is 3.

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