Question

A student uses the quadratic formula to solve a quadratic equation and determines that one of the solutions is x equals negative seven plus square root of negative 99 end square root. What are the values of a and b if this solution is written in the form x = a + bi, where a and b are real numbers?

Answer 1

HELP PLEASE

Answer 2

Bit of factoring is all that's required. You are given\[x=-7 + \sqrt{-99}\]Let's do some factoring using the rules of working with radicals.\[x=-7 + \sqrt{99}\sqrt{-1}\]You OK with that so far?

Answer 3

yes

Answer 4

Good. Now, are you able to simplify \(\sqrt{99}\) ?

Answer 5

3√ 11

Answer 6

right?

Answer 7

Excellent. And do you know what \(\sqrt{-1}\) is?

Answer 8

1

Answer 9

No. The square root of -1 is the imaginary number i. It is referred to in the question. Have you seen it before?

Answer 10

oh yes!

Answer 11

OK. So now your question looks like\[x=-7 + \sqrt{99}\sqrt{-1}\]\[x=-7+3\sqrt{11}i\]Compare this with\[x=a+bi\]What are the values of a and b?

Answer 12

a=-7 b=3√11

Answer 13

Fantastic. Good job!

Answer 14

Thank you sooo much :))))

Answer 15

You're welcome.