+1246 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 4x2+7x+k.
| a=4,b=7,c=k;x1,2=−b±√b2−4ac2a | Substitute in the appropriate values into the formula. |
| x1,2=−7±√72−4∗4∗k2∗4 | Simplify. |
| x1,2=−7±√49−16k8 | |
Obviously, we do not know what k is, but we do know that the roots of the quadratic with the unknown k are x1,2=−7±i√158.
Do you think you can take it on from here?
