Question

find the roots of the quadratic equation by factorisation method ​

Answer 1

Answer:

8x-1=0

•°•x=1/8 (Answer)

Step-by-step explanation:

In the above Image.

Answer 2

$\text{The given quadratic equation is }2x^{2} - \dfrac{x}2 + \dfrac{1}{32} = 0$

$\text{Let us first simplify the equation to make things easier}$

$\text{Lets multiply both sides with }32$

$\implies 32\text{\huge{(}}2x^{2} - \dfrac{x}{2} + \dfrac{1}{32}\text{\huge{)}} = 32(0)$

$\implies 32(2x^{2}) - 32\text{\huge{(}} \dfrac{x}{2}\text{\huge{)}} + 32\text{\huge{(}}\dfrac{1}{32}\text{\huge{)}} = 0$

$\implies 64x^{2} - 16x + 1 = 0$

$\text{Factorisation method suggests we find the prime factors of }\\\text{the product of the coefficient of }x^{2} \text{ and the constant}$

$\implies \text{We must find the prime factors of }64 \times 1 = 64$

$\implies \text{Prime factors of }64 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 2^{6}$

$\text{Now we must express the middle term as sum/subtraction of the prime factors}$

$\text{The middle term is }-16$

$\text{We can ignore the negative in the middle term to avoid confusion, but we}\\\text{must later multiply it after expressing}$

$\implies \text{The middle terms is }16$

$\text{Now we must express the middle term as sum/subtraction of the prime factors}$

$\text{We can see that }2^{3} + 2^{3} = 8 + 8 = 16$

$\implies \text{We can write }16 \text{ as }(8 + 8)$

$\implies \text{We can write }(-16) \text{ as }\{-(8+8)\}$

$\text{Substituting that in the equation}$

$\implies 64x^{2} - (8+8)x + 1 = 0$

$\implies 64x^{2} - 8x-8x + 1 = 0$

$\text{We can take }8x \text{ common in the first two terms and (-1) common in the last two}$

$\implies 8x(8x - 1) -1(8x-1) = 0$

$\text{Taking }(8x-1) \text{ common}$

$\implies(8x-1)(8x-1)= 0$

$\implies\boxed{(8x-1)^{2} = 0}$