A Simple Quadratic Equation Problem.

Algebra Level 3

If x = − 2 x=-2 is a root of the equation 3 x 2 + 7 x + p = 0 3x^2 + 7x + p = 0 . Find the negative value of k k in the equation x 2 + k ( 4 x + k − 1 ) + p = 0 x^2 + k(4x + k-1) + p = 0 if its roots are equal.


The answer is -1.

Jake Roosenbloom by jake roosenbloom , 21, India

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1 solution

Jake Roosenbloom
Dec 27, 2015

Substituting the value of x in the first equation:

We get:

Now, roots (solutions) of the equation are equal. [I already took p as 2]

So, we can safely say that

Therefore,

=>

=>

=>

And finally,

and also − 1 \boxed{-1}

(And in case the question asked only for the negative value k. Therefore the final answer will be -1)

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