If 16x^2 - 24x + k = 0 has two roots (a double root) equal to 3/4, 4 = ?
I don't know what you are talking about, but the two real roots must be 3/4, and 9.
That was my mistake. It was supposed to say k=?
To find the value of k, we can use the fact that the given equation has a double root at 3/4.
A double root means that the quadratic equation can be written in the form (x - r)^2 = 0, where r is the root. In this case, the root is 3/4.
Expanding (x - r)^2, we get:
(x - 3/4)^2 = 0
(x - 3/4)(x - 3/4) = 0
x^2 - (3/4)x - (3/4)x + (3/4)(3/4) = 0
x^2 - (6/4)x + 9/16 = 0
Comparing this quadratic equation with the given equation, we can see that k = 9/16.
Therefore, 4 is equal to 9/16.
To find the value of k, we can make use of the fact that the quadratic equation has a double root at 3/4.
First, let's recall what it means for the equation to have a double root. It means that when we solve the equation, we will get the same value twice. In this case, the double root is 3/4. So, we can set our equation equal to zero:
16x^2 - 24x + k = 0
Now, since 3/4 is a double root, it means that if we substitute 3/4 into our equation for x, we should get zero. Let's do that:
16(3/4)^2 - 24(3/4) + k = 0
Simplifying:
16(9/16) - 72/4 + k = 0
9 - 18 + k = 0
-9 + k = 0
To isolate k, let's add 9 to both sides of the equation:
k = 9
So, k is equal to 9.