How to determine the value of k of the trinomial that is a perfect square?
9x^2 + kx + 49

Question

How to determine the value of k of the trinomial that is a perfect square?
9x^2 + kx + 49

parthkohli · Answer

Recall that $(3x + 7)^2 = 9x^2 + \cdots+49$.

ajprincess · Answer

If $ax^2+bx+c$ is a perfect square then
$b=2*\sqrt a*\sqrt c$
here a=9 and c=49
Does that help @peekaboopork

mathstudent55 · Answer

(a + b)^2 = a^2 + 2ab + b^2
9x^2 = (3x)^2
49 = 7^2

(3x + 7)^2 = 9x^2 +42x + 49
(3x - 7)^2 = 9x^2 - 42x + 49

k = 42 or k = -42

parthkohli · Answer

A good way to find the middle term is to realize that in a perfect square, $2ab$ is the middle term where $(a  +b)^2  = a^2 + 2ab + b^2$. Here, $b^2= 49 \iff b = 7$ and $a^2 = 9x^2 \iff a = 3x $.

parthkohli · Answer

So what would $2\cdot 7\cdot 3x$ be?

parthkohli · Answer

Actually I should have put $\pm$, but it still would have the same result!