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# Factorize Each of the Following Quadratic Polynomials by Using the Method of Completing the Square: 4x2 − 12x + 5 Answer 8: - Mathematics

Sum

Factorize each of the following quadratic polynomials by using the method of completing the square:
4x2 − 12x + 5

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#### Solution

$4 x^2 - 12x + 5$
$= 4( x^2 - 3x + \frac{5}{4}) [\text{ Making the coefficient of } x^2 = 1]$
$= 4[ x^2 - 3x + \left( \frac{3}{2} \right)^2 - \left( \frac{3}{2} \right)^2 + \frac{5}{4}] [\text{ Adding and subtracting }\left( \frac{3}{2} \right)^2 ]$
$= 4[(x - \frac{3}{2} )^2 - \frac{9}{4} + \frac{5}{4}] [\text{ Completing the square }]$
$= 4[(x - \frac{3}{2} )^2 - 1^2 ]$
$= 4[(x - \frac{3}{2}) - 1][(x - \frac{3}{2}) + 1]$
$= 4(x - \frac{3}{2} - 1)(x - \frac{3}{2} + 1)$
$= 4(x - \frac{5}{2})(x - \frac{1}{2})$
$= (2x - 5)(2x - 1)$

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#### APPEARS IN

RD Sharma Class 8 Maths
Chapter 7 Factorization
Exercise 7.9 | Q 8 | Page 33
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