Question

Root of quardatic equation of 2x²+½=2x

Answer 1

Answer:

½

Step-by-step explanation:

Given a quadratic equation such that,

$2 {x}^{2} + \frac{1}{2} = 2x$

Further simplifying, we get,

$= > 2 {x}^{2} - 2x + \frac{1}{2} = 0 \\ \\ = > 4 {x}^{2} - 4x + 1 = 0$

To find the roots,

We will apply middle term splitting method.

Therefore,we will get,

$= > 4 {x}^{2} - 2x - 2x + 1 = 0$

Taking out common terms, we get,

$= > 2x(2x - 1) - 1(2x - 1) = 0 \\ \\ = > (2x - 1)(2x - 1) = 0 \\ \\ = > {(2x - 1)}^{2} = 0 \\ \\ = > 2x - 1 = 0 \\ \\ = > 2x = 1 \\ \\ = > x = \frac{1}{2}$

Hence, the required zero is ½.