# root of the equation

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• February 26th 2010, 01:38 AM
mastermin346
root of the equation
(p^2)(x^2)-12x+p+7=0 has the root 3/2..find the value of p.

please help,show step by step the answer that u get..thanks
• February 26th 2010, 03:49 AM
HallsofIvy
Quote:

Originally Posted by mastermin346
(p^2)(x^2)-12x+p+7=0 has the root 3/2..find the value of p.

please help,show step by step the answer that u get..thanks

Replace x with 3/2. The result will be a quadratic equation for p. Solve that equation.
• February 26th 2010, 03:58 AM
Bacterius
To explain HallsOfIvy's solution, remember that the roots of an equation are the values of $x$ when $y = 0$. Here, you are given an equation in the form $y = f(x)$ with $y = 0$ and $f(x) = (p^2)(x^2)-12x+p+7$ for some $p$. Since you are given that one root is $\frac{3}{2}$, you know that when $y = 0$ (which is our case), $x = \frac{3}{2}$. So you can just substitute $x = \frac{3}{2}$ into $f(x)$ and solve for $p$, to find which values of $p$ (there may be more than one) satisfy the equation $f(x) = 0$ when $x = \frac{3}{2}$. :)