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Which constant must be added and subtracted to solve the quadratic equation 9x2+34x-2 = 0 by the method of completing the square? - Mathematics

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MCQ

Which constant must be added and subtracted to solve the quadratic equation `9x^2 + 3/4x - sqrt(2)` = 0 by the method of completing the square?

Options

  • `1/8`

  • `1/64`

  • `1/4`

  • `9/64`

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Solution

`1/64`

Explanation:

Given equation is `9x^2 + 3/4x - sqrt(2)` = 0

`(3x)^2 + 1/4 (3x) - sqrt(2)` = 0

On putting `3x = y`

We have `y^2 + 1/4y - sqrt(2)` = 0

`y^2 + 1/4y + (1/8)^2 - (1/8)^2 - sqrt(2)` = 0

`(y + 1/8)^2 = 1/64  + sqrt(2)`

`(y + 1/8)^2 = (1 + 64 sqrt(2))/64`

Thus, `1/64` must be added and subtracted to solve the given equation.

Concept: Nature of Roots
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APPEARS IN

NCERT Mathematics Exemplar Class 10
Chapter 4 Quadatric Euation
Exercise 4.1 | Q 7 | Page 37
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