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If the sum of the roots of the equation negative three π₯ squared plus ππ₯ plus 11 equals zero is four, what is value of π?
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So, what we have in this question is a quadratic thatβs in a nice useful form cause itβs in the form ππ₯ squared plus ππ₯ plus π equals zero.
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But why is this useful?
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Well, itβs useful because what we have are a couple of relationships relating to the roots of an equation.
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First of all, the sum of the roots are equal to negative π over π.
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And the product of the roots are equal to π over π.
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And we see that weβve got our π, π, and π when we have our quadratic in the form ππ₯ squared plus ππ₯ plus π equals zero.
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Well, the first thing we always do is identify our π, π, and π.
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So, we have our negative three for our π, π for our π, and 11 for our π.
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Itβs worth mentioning at this point that the sign is very important.
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Hence, for π, weβve got negative three not just three.
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Okay, weβve got a, π, and π.
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Whatβs next?
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Well, weβre told in the question that the sum of the roots is four.
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So therefore, weβre gonna use the relationship that tells us that sum of the roots is equal to negative π over π.
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So therefore, what weβre gonna have when we substitute in our values is four, cause thatβs our sum, is equal to negative π over negative three.
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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.
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So, great, weβre 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.
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And when we do that, what weβre gonna get is 12 is equal to π.
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So therefore, what we can say is that if the sum of the roots of the equation negative three π₯ squared plus ππ₯ plus 11 equals zero is four, then the value of π is 12.