Question

39.
Roots of quadratic equation 2x²-x+1/8 are:​

Answer 1

Answer:

x = $\frac{1}{4}$ and x = $\frac{1}{4}$

Step-by-step explanation:

$2 {x}^{2} - x + \frac{1}{8} = 0 \\ \\ = > 16 {x}^{2} - 8x + 1 = 0(multipling \: with \: 8) \\ \\ = > 16 {x}^{2} - (4 + 4)x + 1 = 0 \\ \\ = > 16 {x}^{2} - 4x - 4x + 1 = 0 \\ \\ = > 4x(4x - 1) - 1(4x - 1) = 0 \\ \\ = > (4x - 1)(4x - 1) = 0 \\ \\ \\ \\ 4x - 1 = 0 \\ \\ = > x = \frac{1}{4} \\ \\ \\ \\ \\ 4x - 1 = 0 \\ \\ = > x = \frac{1}{4}$

Answer 2

$\underline{ \underline{ \bf GIVEN \: \: EQUATION : }}$

$\boxed{ \bf 2 {x}^{2} - x + \frac{1}{8} = 0 }$

$\large \underline{ \underline{ \bf Solution : }}$

$\bf Both \: side \: multiply \: by \: 8$

$16 {x}^{2} - 8x + 1 = 0 \\ \bf{By \: splitting \: middle \: term} \\ \\ 16 {x}^{2} - 4x - 4x + 1 = 0 \\ \\ 4x(4x - 1) - 1(4x - 1) = 0 \\ \\ (4x - 1)(4x - 1) = 0 \\ \\ \boxed {\red{ \bf x = \frac{1}{4}} }$