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

1. ParthKohli

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

2. ajprincess

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

3. mathstudent55

(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

4. ParthKohli

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 $$a^2 = 9x^2 \iff a = 3x$$.

5. ParthKohli

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

6. ParthKohli

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