Intermediate Quadratic Equations If n is a constant and if there exists a unique value of m for

kabutjv7

kabutjv7

Answered question

2022-04-24

Intermediate Quadratic Equations
If n is a constant and if there exists a unique value of m for which the quadratic equation x2+mx+(m+n)=0 has one real solution, then find n.
Let the roots of the quadratic be r, s. Vieta gives m=r+s,m+n=rs. Thus, n=rs+r+sn+1=(n+1)(m+1). From here, I don't know what to do. I have a feeling that the factoring trick was unnecessary.

Answer & Explanation

kweefomucy9

kweefomucy9

Beginner2022-04-25Added 13 answers

There is a single real solution when
m24(m+n)=0,
(m2)244n=0
and this equation has a single solution in mn=1.

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