+1245 If the two roots of the quadratic $4x^2+7x+k$ are $\frac{-7\pm i\sqrt{15}}{8}$, what is $k$?
+2446 Hello, Lightning!
The quadratic formula is a formula that solves for the roots of any quadratic. Let's apply it to the quadratic \(4x^2+7x+k\).
| \(a=4, b=7, c=k;\\ x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\) | Substitute in the appropriate values into the formula. |
| \(x_{1,2}=\frac{-7\pm\sqrt{7^2-4*4*k}}{2*4} \) | Simplify. |
| \(x_{1,2}=\frac{-7\pm\sqrt{49-16k}}{8}\) | |
Obviously, we do not know what k is, but we do know that the roots of the quadratic with the unknown k are \(x_{1,2}=\frac{-7\pm i\sqrt{15}}{8}\).
Do you think you can take it on from here?
