If 25x²+k+9 is a perfect square find k
(b/2)^ 2=ac
so k^2/2=25X9
=225
225X4=900
k^2=900
so k=30
To determine the value of k, we need to find the perfect square trinomial that matches the expression 25x² + k + 9.
A perfect square trinomial can be written in the form (ax + b)², where a represents the square root of the coefficient of the x² term and b represents half of the coefficient of the x term.
So, for our given expression, 25x² + k + 9, let's compare it to (ax + b)².
The coefficient of the x² term in the expression is 25. The square root of 25 is 5. Therefore, a = 5.
Now, to determine b, we need to find half of the coefficient of the x term. In our case, there is no x term, so the coefficient is 0. Half of 0 is also 0. Therefore, b = 0.
Now, we can rewrite our perfect square trinomial as (5x + 0)², which simplifies to (5x)².
Comparing this to the given expression, (5x)² is equal to 25x².
Since k + 9 is the remaining part after subtracting the x² term, we can conclude that k + 9 = 0, and thus k = -9.
Therefore, when 25x² + k + 9 is a perfect square, the value of k is -9.
well, 25=5^2 and 9=3^2, so try
(5x+3)^2 = ?
Note that you will get two answers.