Question

factorise x²+x+1/4
please answer​

Answer 1

(x+1/2)(x+1/2).

Step-by-step explanation:

We've to factorise

$x {}^{2} + x + (1 \div 4)$

By using quadratic formula

$x = ( - b \frac{ + }{ - } \sqrt{b {}^{2} - 4ac } ) \div 2a$

here a = 1 as coefficient of x² = 1

b = 1 as coefficient of x = 1

and c = 1/4

let's use quadratic formula to factorise x² + x + 1/4

$x = ( - 1 \frac{ + }{ - } \sqrt{1 {}^{2} - 4(1)(1 \div 4) } ) \div 2(1) \\ x = ( - 1 \frac{ + }{ - } \sqrt{1 - 1} ) \div 2 \\ x = ( - 1 \frac{ + }{ - } \sqrt{0} ) \div 2 \\ x = - 1 \div 2 \\ therefore \: factors \: of \: x {}^{2}+ x + (1 \div 4) \\ = > | x + (1 \div 2) | {}^{2}$

=> Factors are ( x + 1/2 ) × ( x + 1/2 )

please mark me brainiest