How do you find the constant, $k$ $k$ , to make the expression $x^{2} + 5 x + k$ $x^2 + 5x +k$ a perfect square trinomial?

Question

How do you find the constant, $k$ $k$ , to make the expression $x^{2} + 5 x + k$ $x^2 + 5x +k$ a perfect square trinomial?

1 Answer

Impact of this question

5734 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-04-08T13:12:36

A perfect (trinomial) square, with unit coefficient on the $x^{2}$ $x^2$ term, is of the form:
${(x + a)}^{2} = x^{2} + 2 a x + a^{2}$ $(x+a)^2 = x^2+2ax+a^2$

The third term (the one that does not include the $x$ $x$ ) is therefore
the square of (half of the coefficient of the $x$ $x$ term).

That is, for our example,
$k = {(\frac{5}{2})}^{2} = \frac{25}{4}$ $k = (5/2)^2 = (25)/(4)$

Science

Math

Humanities

... and beyond

How do you find the constant, $k$ $k$ , to make the expression $x^{2} + 5 x + k$ $x^2 + 5x +k$ a perfect square trinomial?

1 Answer

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you find the constant, kkk, to make the expression x^2 + 5x +kx2+5x+kx^2 + 5x +k a perfect square trinomial?

1 Answer

Related questions

Impact of this question

How do you find the constant, $k$ $k$ , to make the expression $x^{2} + 5 x + k$ $x^2 + 5x +k$ a perfect square trinomial?