Answer each question. Find the values of a, b, and c for which th...

Question

Answer each question. Find the values of a, b, and c for which the quadratic equation. 
ax^2 + bx + c = 0 has the given numbers as solutions. (Hint: Use the zero-factor property in reverse.) 4, 5

Accepted Answer

Hey, everyone in this problem we're told to suppose three and two are the solutions of the equation A X squared plus BX plus C equals zero. And we're asked to find the values of A B and C. Alright, let's start with the first term. Okay. If X is equal to three is a solution or X is equal to two is a solution, we can rearrange this, This means that X -3 is equal to zero or X minus two Is equal to zero. If we need one of these terms equal to zero, then multiplying them together. Okay. We'll ensure that we're equal to zero. We either have X -3 or zero or we have X -2 is zero. Okay, no matter which one is zero, we're multiplying together. And so the product will be zero. Now, we can expand this. We know that this is a factored form of a quadratic equation. We can expand it to write it in the standard form X squared plus BX plus C equals zero and compare those coefficients. So if we expand this, we're gonna have X squared, We're gonna have -3X We're gonna have -2, X plus six is equal to zero. A simplifying X squared minus five, X plus six is equal to zero. And then we can compare our coefficients. Okay. So the coefficient on the X squared term is going to be A, so we have that A is equal to one. The coefficient on the X term is going to be B so that B is equal to negative five, don't miss that minus sign. And we have C which is going to be the constant term and that's going to be equal to six. And so the values of A B and C that represent this equation are one negative five and six and that is going to correspond with answer choice A. That's it for this one. Thanks everyone for watching. See you in the next video.

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Answer each question. Find the values of a, b, and c for which the quadratic equation. ax^2 + bx + c = 0 has the given numbers as solutions. (Hint: Use the zero-factor property in reverse.) 4, 5