1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

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

Open in App
Solution

## $4{x}^{2}-12x+5\phantom{\rule{0ex}{0ex}}=4\left({x}^{2}-3x+\frac{5}{4}\right)\left[Makingthecoefficientof{x}^{2}=1\right]\phantom{\rule{0ex}{0ex}}=4\left[{x}^{2}-3x+{\left(\frac{3}{2}\right)}^{2}-{\left(\frac{3}{2}\right)}^{2}+\frac{5}{4}\right]\left[Addingandsubtracting{\left(\frac{3}{2}\right)}^{2}\right]\phantom{\rule{0ex}{0ex}}=4\left[\left(x-\frac{3}{2}{\right)}^{2}-\frac{9}{4}+\frac{5}{4}\right]\left[Completingthesquare\right]\phantom{\rule{0ex}{0ex}}=4\left[\left(x-\frac{3}{2}{\right)}^{2}-{1}^{2}\right]\phantom{\rule{0ex}{0ex}}=4\left[\left(x-\frac{3}{2}\right)-1\right]\left[\left(x-\frac{3}{2}\right)+1\right]\phantom{\rule{0ex}{0ex}}=4\left(x-\frac{3}{2}-1\right)\left(x-\frac{3}{2}+1\right)\phantom{\rule{0ex}{0ex}}=4\left(x-\frac{5}{2}\right)\left(x-\frac{1}{2}\right)\phantom{\rule{0ex}{0ex}}=\left(2x-5\right)\left(2x-1\right)$

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Introduction
MATHEMATICS
Watch in App
Join BYJU'S Learning Program