Question

factorise
x²+x/4 - 1/8​

Answer 1

$\huge\boxed{\fcolorbox{black}{pink}{Answer}}$

x²+x/4-1/8 = (x+1/2)(x-1/4)

$\huge\mathcal\colorbox{golden}{{\color{black}{★explanation★}}}$

Given quadratic polynomial:

x²+x/4-1/8

Splitting the middle term, we get

= x²+x/2-x/4 -1/8

= x(x+1/2)-1/4(x+1/2)

= (x+1/2)(x-1/4)

Therefore,

x²-x/4-1/8 = (x+1/2)(x-1/4)

Answer 2

$\huge\star\underline{\mathtt\red{A}\mathtt\green{N}\mathtt\blue{S}\mathtt\purple{W}\mathtt\orange{E}\mathtt\pink{R}}\star\:$

$\large {x}^{2} + \frac{x}{4} - \frac{1}{8} = 0$

Multiplying both the sides by 8,

$\longrightarrow \large( {x}^{2} + \frac{x}{4} - \frac{1}{8} )8 = 0 \times 8$

$\longrightarrow \large {8x}^{2} + 2x - 1 = 0$

$\longrightarrow \large {8x}^{2} +( 4x - 2x) - 1 = 0$

$\longrightarrow \large4x(2x + 1) - 1(2x + 1) = 0$

$\longrightarrow \large(2x + 1)(4x - 1) = 0$

Either x = $\large{\dfrac{-1}{2}}$

OR

x = $\large{\dfrac{1}{4}}$