# Thread: Roots of equation?

1. ## Roots of equation?

Find the value of p and the roots of the equation 2xsquared - 33x + p = 0
given that one root is ten times the other root.
I dont how to start this question, can someone help me please.
Thanks!

2. Originally Posted by Detanon
Find the value of p and the roots of the equation 2xsquared - 33x + p = 0
given that one root is ten times the other root.
I dont how to start this question, can someone help me please.
Thanks!
You can use the caret symbol ^ to signify "to the power of". This sign also works in LaTeX

2x^2 - 33x+p=0

Use the quadratic formula

$x = \frac{33\pm \sqrt{1089-8p}}{4}$

Split the $\pm$ sign to see the two roots more clearly.

For the fun of it I will choose the positive root to be bigger than the negative root although either should work

$x_1 = \frac{33+\sqrt{1089-8p}}{4}$

$x_2 = \frac{33-\sqrt{1089-8p}}{4}$

$x_1=10x_2 \: \rightarrow \: \: \frac{33+\sqrt{1089-8p}}{4} = 10 \cdot \frac{33-\sqrt{1089-8p}}{4}$

Solve for p (and the denominator will cancel immediatly)

3. How do you solve for p..?

4. Originally Posted by Detanon
How do you solve for p..?
Multiply the final equation by 4. Then solve $33 + \sqrt{a} = 10 (33 - \sqrt{a})$ for $a$ where $a = 1089 - 8p$. Then use the value of $a$ to solve for $p$.