# Question Video: Finding the Value of an Unknown in a Quadratic Equation by Using the Relation between Its Coefficient and Its Roots Mathematics

If the sum of the roots of the equation β3π₯Β² + ππ₯ + 11 = 0 is 4, what is value of π?

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### Video Transcript

If the sum of the roots of the equation negative three π₯ squared plus ππ₯ plus 11 equals zero is four, what is value of π?

So, what we have in this question is a quadratic thatβs in a nice useful form cause itβs in the form ππ₯ squared plus ππ₯ plus π equals zero. But why is this useful? Well, itβs useful because what we have are a couple of relationships relating to the roots of an equation. First of all, the sum of the roots are equal to negative π over π. And the product of the roots are equal to π over π. And we see that weβve got our π, π, and π when we have our quadratic in the form ππ₯ squared plus ππ₯ plus π equals zero.

Well, the first thing we always do is identify our π, π, and π. So, we have our negative three for our π, π for our π, and 11 for our π. Itβs worth mentioning at this point that the sign is very important. Hence, for π, weβve got negative three not just three. Okay, weβve got a, π, and π. Whatβs next?

Well, weβre told in the question that the sum of the roots is four. So therefore, weβre gonna use the relationship that tells us that sum of the roots is equal to negative π over π. So therefore, what weβre gonna have when we substitute in our values is four, cause thatβs our sum, is equal to negative π over negative three. Well, we know that a negative divided by a negative is a positive, so we can rewrite negative π over negative three as just π over three.

So, great, weβre now in a position where we can find π quite easily because all we need to do is multiply both sides of our equation by three. And when we do that, what weβre gonna get is 12 is equal to π.

So therefore, what we can say is that if the sum of the roots of the equation negative three π₯ squared plus ππ₯ plus 11 equals zero is four, then the value of π is 12.