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.) i, -i

Accepted Answer

Hey, everyone. Welcome back in this problem. We're told to suppose that to I and negative two, I 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 choices are A, A is equal to zero. B is equal to one and C is equal to four. B A is equal to one, B is equal to zero and C is equal to four C A is equal to one. B is equal to four and C is equal to zero and D A is equal to four. B is equal to zero and C is equal to one. Now, if these are solutions to the equation A X squared plus BX plus C equals zero, that means that we can write X is equal to two I Or X is equal to -2. Now, we want to write this as an equation equal to zero. So let's rearrange these terms X is equal to two, I, we can move the two I to the left hand side and write this as X minus two, I is equal to zero. Or same thing here. Move the negative two I to the left hand side. It's going to give us X plus two I is equal to zero. Now, we have two terms equal to zero. They're both linear terms. We want to get a quadratic equation. And so what we can do is we can multiply them. We have X minus two I times X plus two. I. Now we either have X minus two equal to zero or we have X plus two is equal to zero. Now, as long as either of them is zero, the product is going to be zero. And so we have X minus two I times X plus two, I is going to be zero. Now, this looks like a factored quadratic equation. Okay. So let's go ahead and expand, write it out in the form X squared plus BX plus C equals zero so that we can compare those coefficients to find the values of A B and C. So we expand, we're going to have X squared -2 IX Plus two IX minus four I squared is equal to zero. So these terms in the middle negative two I X plus two I X, those will add up to zero. We're left with X squared minus four. Now the value of I squared is negative one. Can we know that I is equal to the square root of negative one? And so I swear it is going to be equal to negative one. So we get X squared minus four times negative one is equal to zero, which gives us X squared plus four is equal to zero. Now, if we compare our coefficients, A is gonna be the coefficient on the X squared term. In our case, that's one B is going to be the coefficient on the extra. In our case that zero, we don't have a linear term and C is going to be the coefficient of the constant or just that constant term in our case is four. And so we have A is equal to one B is equal to zero and C is equal to four. And that is going to correspond with answer choice B. Thanks everyone for watching. I hope this video helped see you in the next one.

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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.) i, -i