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If 12 a root of the equation x2+kx-54 = 0, then the value of k is ______. - Mathematics

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MCQ
Fill in the Blanks

If `1/2` a root of the equation `x^2 + kx - 5/4` = 0, then the value of k is ______.

Options

  • 2

  • – 2

  • `1/4`

  • `1/2`

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Solution

If `1/2` a root of the equation `x^2 + kx - 5/4` = 0, then the value of k is 2.

Explanation:

If `1/2` is a root of the equation

x2 + kx – `5/4` = 0 then

Substituting the value of `1/2` in place of x should give us the value of k.

Given, x2 + kx – `5/4` = 0 where, x = ½

`(1/2)^2 + k(1/2) - (5/4)` = 0

`(k/2) = (5/4) – 1/4`

k = 2

Concept: Nature of Roots
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APPEARS IN

NCERT Mathematics Exemplar Class 10
Chapter 4 Quadatric Euation
Exercise 4.1 | Q 4 | Page 37
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