Question

If 1/2 is a root of x2 + px - 5 / 4 = 0, then the value of p is
(a) 2 (b) - 2
(c) 1 / 4 (d) 1 / 2

Answer 1

Answer:

Given

1/2 is a root

${x}^{2} + px - \frac{5}{4} = 0 \\ \\ substitute \: x = \frac{1}{2} \: in \: the \: given \: equation \\ \\ { (\frac{1}{2}) }^{2} + p( \frac{1}{2} ) - \frac{5}{4} = 0 \\ \\ \frac{1}{4} + \frac{p}{2} - \frac{5}{4} = 0 \\ \\ \frac{p}{2} = \frac{5}{4} - \frac{1}{4} \\ \\ \frac{p}{2} = \frac{5 - 1}{4} \\ \\ \frac{p}{2} = \frac{4}{4} \\ \\ \frac{p}{2} = 1 \\ \\ p = 2$

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Answer 2

Answer :

If 1/2 is a root of x2 + px - 5 / 4 = 0, then the value of p is 2.

Put value of x as 1/2.

⇒ (1/2)² + (1/2)p - 5/4 = 0

⇒ 1/4 - 5/4 +1p/2 = 0

⇒ 1 - 5 + 2p/4 = 0

⇒ -4 + 2p/4 = 0

⇒ -4 + 2p = 0

⇒ 2p = 4

⇒ p = 4/2

⇒ p = 2

$\rule{200}{2}$