Question

solve equation using factorising method 2 x square - 1 / 2 x = 0​

Answer 1

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



Dividing 2 on both sides.

x² - x = 0

Taking x common out from the given equation.

x(x - 1) = 0

x - 1 = x $\times$ 0

x - 1 = 0

$\boxed{\bold{x = 1}}$

(Or)

x = 0 $\times$ x - 1

$\boxed{\bold{x = 0}}$

Here, in the given expression, x can be either 1 or 0.

By equating 1 in the place of x in the given expression.

x² - x = 0

(1)² - 1 = 0

1 - 1 = 0

0 = 0

$\boxed{\bold{L.H.S = R.H.S.}}$

Equating 0 in the place of x in the following equation.

x² - x = 0

(0)² - 0 = 0

0 - 0 = 0

0 = 0

$\boxed{\bold{L.H.S = R.H.S}}$

Therefore, the zeros of the given quadratic equation are 1 and 0.

$\boxed{\bold{Remember:}}$

A quadratic equation can have no solutions (zeros), 1 solutions and maximum 2 zeros.

Answer 2

x is equal to whole root x by 2

$2x ^{2} - x \: = \: 0 \\ 2x {}^{2} \: = \: 0 \\ x {}^{2} = x \div 2 \\ x = \sqrt{x \div 2}$

hence proved