# How do you factor and solve x^2−(7/2)x+3/2=0?

May 20, 2016

(1/2)(x - 3)(2x - 1)

#### Explanation:

$y = {x}^{2} - \left(\frac{7}{2}\right) x + \frac{3}{2} = 0$
Find 2 fractions knowing sum $\left(b = - \frac{7}{2}\right)$ and product $\left(c = \frac{3}{2}\right)$.
By guessing, they are the 2 fractions: $- \frac{3}{1} \mathmr{and} - \frac{1}{2}$.
Sum:$- \frac{3}{1} - \frac{1}{2} = - \frac{6}{2} - \frac{1}{2} = - \frac{7}{2}$
Product:$\left(- \frac{3}{1}\right) \left(- \frac{1}{2}\right) = \frac{3}{2}$
Factored form of y.
$y = \left(x - 3\right) \left(x - \frac{1}{2}\right) = \left(\frac{1}{2}\right) \left(x - 3\right) \left(2 x - 1\right)$
There are 2 real roots: x = 3 and x = 1/2