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If the two roots of the quadratic $4x^2+7x+k$ are $\frac{-7\pm i\sqrt{15}}{8}$, what is $k$?

 Jun 5, 2018
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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? 

 Jun 5, 2018

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