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.) -3, 2

Accepted Answer

Hey, everyone in this problem we're told to suppose that negative four and six 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. The answer traces were given are A, A is equal to one. B is equal to two and C is equal to 24. B is equal to one, B is equal to two and C is equal to negative 24. C A is equal to one. B is equal to negative two and C is equal to negative D A is equal to one. B is equal to negative two and C is equal to positive 24. Alright, let's get started. So if negative four and six are solutions to X squared plus BX plus C equals zero, that means that either X is equal to negative four Or X is equal to six. Okay. These are the solutions and we have X equals of those things. Well, we can rearrange these okay. If we move the negative board to the left hand side, we get that X plus four is equal to zero Or X -6 is equal to zero. We have these two terms, either of them is equal to zero. If we multiply them together, okay, we know at least one of them is zero. If one of them is zero, then the product of the two will be zero. And so The product will be equal to zero. Okay. This will satisfy the equation. Now you'll recognize this, this looks like the factored form of a quadratic. So let's go ahead and expand, get our quadratic in this standard form A X squared plus BX plus C. And then we can compare the coefficients in order to find the values of A B and C. So if we expand here, we're gonna have X squared minus six X plus four, X minus 24 is equal to zero. Simplifying gives us X squared minus six, X plus four. X is going to give us minus two X and then we have our minus 24 is equal to zero. And if we compare our coefficients to the standard form X squared plus BX plus C is equal to zero, we see that A, the coefficient on the X squared term is one B, the coefficient on the x term is -2. And see the constant term is negative 24. And those are A B and C values. If we look at our answer choices, we see that this is going to correspond with answer choice C we have A is equal to one B is equal to negative two and C is equal to negative 24. 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.) -3, 2