# Math Help - equations and quadratic functions

1. ## equations and quadratic functions

1) If x² + mx + n is a perfect square, show that m²=4n

and

2) find value of k

x² + (2k+10)x + k² + 5 = 0

Help would be much appreciated. Thanks.

2. Hello, lra11!

1) If $x^2 + mx + n$ is a perfect square, show that: . $m^2 = 4n$

If $x^2+mx+n$ is a square, the equation $x^2 + mx + n \:=\:0$ has one root.

If a quadratic equation has one root, its discriminant $(b^2-4ac)$ is zero.

Hence: . $m^2 - 4n \:=\:0$

Therefore: . $m^2\:=\:4n$

2) Find value of $k$

. . $x^2 + (2k+10)x + k^2 + 5 \:= \:0$

What are the conditions for this quadratic equation?

As given, $k$ can be any number $\geq -2$.

3. Originally Posted by lra11
remember what you do when you are completing the square? if a quadratic is a complete square, it means that the constant is the square of 1/2 of the coefficient of x. thus, if $x^2 + mx + n$ is a complete square, it follows immediately that $n = \left( \frac m2 \right)^2$ and the rest is trivial