# Question Video: Finding the Value of an Unknown in a Quadratic Equation given One of Its Roots Mathematics

Given that π₯ = β9 is a root of the equation π₯Β² + ππ₯ = 36, determine the value of π.

03:21

### Video Transcript

Given that π₯ equals negative nine is a root of the equation π₯ squared plus ππ₯ equals 36, determine the value of π.

Well, the first thing weβre gonna do is weβre gonna look at π₯ squared plus ππ₯ equals 36. And we can see that, in fact, what we can do with this is rewrite it in a quadratic equation form. So if we subtract 36 from each side of the equation, what weβll do is see our quadratic in a form weβre more used to. So weβve got π₯ squared plus ππ₯ minus 36 is equal to zero. So what weβre told in the question is that π₯ is equal to negative nine is a root of the equation. So therefore, what we can do is rewrite our quadratic equation in factored form. And when we do that, weβre gonna have π₯ plus nine multiplied by π₯ plus π, so some number, is equal to zero. And thatβs because we only know one of the roots of our equation.

You might think, well, how do we know that the left-hand parentheses in our factored form was π₯ plus nine? Well, we know that if π₯ is equal to negative nine is a root, then when weβre writing a quadratic in factored form, the value of π₯ is going to be whatβs required to make each of the parentheses equal to zero. So if π₯ is equal to negative nine, then negative nine plus nine is equal to zero. Okay, great. But how are we gonna find out our mystery number, our π? Because once we found our π, then weβre gonna be able to find the value of π.

So what weβre gonna do is distribute across our parentheses. And to do this, what we do is multiply everything in the left-hand parentheses by everything in the right-hand parenthesis, which is gonna be first of all π₯ multiplied by π₯, which is π₯ squared, then π₯ multiplied by π, which is ππ₯, then positive nine multiplied by π₯, which is nine π₯, and then finally nine multiplied by π, which is nine π. So weβve got this all equal to zero. Okay, so now whatβs our next step? Well, if we take a look at the original equation, so our original quadratic, weβve got π₯ squared plus ππ₯ minus 36 equals zero. So what we can see is that negative 36 is the only non-π₯-containing term. So if we look back at the equation that we form now, what weβve got is positive nine π is the only non-π₯-containing term.

So therefore, what we can do is equate these. So we can say that nine π is equal to negative 36. So therefore, what we can do is divide through by nine to find out what π is. And when we do that, weβre gonna get π is equal to negative four. So now what weβre gonna do is substitute this value of π back in to our equation. So when we do, weβll get π₯ squared minus four π₯ plus nine π₯ minus 36 is equal to zero. So now what we can do is collect like terms, so we can collect negative four π₯ plus nine π₯. So what weβre gonna have is π₯ squared plus five π₯ minus 36 is equal to zero.

Well, if we look at the question, what weβre looking to do is determine the value of π. Well, we can see from our new equation that weβve found the value of π. And that value of π is five, remembering that we need to make sure that we do take into account the sign, and it is positive. So we can say that given that π₯ is equal to negative nine is a root of the equation π₯ squared plus ππ₯ equals 36, then the value of π is five.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.