Quadratic equation!Given that 1/3 is one of the root

Question

$$px^2-4x+p-2=0$$

root=1/3

can anyone tell me how to do step by step im stuck in the middle
$$1/p+p-10/3=0 $$ :D

Answer 1

Since $x = 1/3$ is a root, then plugging $x = 1/3$ into every place $x$ occurs in your quadratic gives: $$p\left(\frac 13\right)^2 - 4\left(\frac 13\right) + p -2= 0$$

Solve for $p$.

$$\frac 19 p - \frac 43+ p = 2 \iff \frac{10}9 p = \frac 43 + 2 \iff p = \frac{9}{10}\cdot \frac {10}{3} = \frac 9 3 = 3$$