I'm having problems with a math question;?

Question

What value of k would make 9x2 + 42x + k a perfect square trinomial?
The answer is k=49... but how do you get that?

Answer 1

9x^2+42x+k
=(3x)^2+2*3x*7+k
Now,you can observe that 42x is equal to 2*3x*7 and we must add another term (7)^2 or 49 to it to make the expression a perfect square.
Hence k=49

Answer 2

The general formula is

( a x + b )^2 = (a^2) (x^2) + 2 a b x + b^2

Your formula is

( a x + b )^2 = 9 x^2 + 42 x + k

Look at them and compare. You get 3 equations:

(1) a^2 = 9

(2) 2 a b = 42

(3) b^2 = k

From these 3 equations you have to calculate a, b and k.

From equation (1) you get a = 3 or a = -3.

Then from equation (2) you get b = 7 or b = -7.

Now from equation (3) you get k = 7^2 = 49 or k = (-7)^2 = 49 (the same result).

OK?

Answer 3

completing the square is pretty simple....
first you need to take out the 9 that is the coefficient of the x^2 term.
9(x^2 + (14/3)x + k)
take half of 14/3 which is 7/3
square 7/3 which is 49/9
and since you are completing the square for 9x^2 + 42x + k
k = 9 * (49/9) which equals 49
the 9 has to be redistributed.

Answer 4

9x^2+42x+k
discriminant=42^2-36k=0
k=42x42/36=7x7=49.

oR
9x^2+42x=k
=(3x)^2=2x3xx7+7^2+k-7^2
=(x+7)^2+k-49
for the given expression to be a perfect square,k-49=0or k=49