FIND THE VALUE OF K, SO THAT THE EXPRESSION IS A PERFECT SQUARE TRINOMIAL.
x^2+6x+k
k=
k=9
find half of 6x then square it
To find the value of k so that the expression x^2 + 6x + k is a perfect square trinomial, we need to use the following formula:
a^2 + 2ab + b^2 = (a + b)^2
In this case, a is the square root of x^2, which is x. And b is half the coefficient of x, which is 6/2 = 3.
So, we will have:
x^2 + 2(x)(3) + 3^2
= x^2 + 6x + 9
To make the expression x^2 + 6x + k a perfect square trinomial, we need to set k = 9.
Therefore, k = 9.
To find the value of k such that the expression x^2 + 6x + k is a perfect square trinomial, we need to complete the square.
A perfect square trinomial can be expressed as the square of a binomial, meaning it can be factored into the form (x + a)^2, where a is a constant.
To get the quadratic expression in the form of a perfect square trinomial, we need to add and subtract a suitable constant to the expression x^2 + 6x + k.
To determine this constant, we take half of the coefficient of x (which is 6) and square it. In this case, (6/2)^2 = 9.
So, to express x^2 + 6x + k as a perfect square trinomial, we add and subtract 9 to the expression:
x^2 + 6x + 9 - 9 + k
Rearranging this, we have:
(x^2 + 6x + 9) + (k - 9)
The expression in parentheses is a perfect square trinomial, specifically (x + 3)^2.
Therefore, the expression x^2 + 6x + k can be rewritten as (x + 3)^2 + (k - 9).
For this to be a perfect square trinomial, the constant term (k - 9) must be zero since adding zero to a perfect square trinomial does not change it.
Therefore, k - 9 = 0, which implies k = 9.
So, the value of k that makes the expression x^2 + 6x + k a perfect square trinomial is k = 9.