Find the roots of the equation.
4x to the second power plus 9=12x
4 x^2 + 9 = 12 x ?
4 x^2 - 12 x + 9 = 0
(2x-3)(2x-3) = 0
x = 1.5 or 1.5 , double root there
To find the roots of the equation 4x^2 + 9 = 12x, we need to rearrange the equation to the form of ax^2 + bx + c = 0, where a, b, and c are coefficients.
Here's how we can do that:
1. Move all terms to one side of the equation:
4x^2 - 12x + 9 = 0
2. Now that we have the equation in the form ax^2 + bx + c = 0, we can use the quadratic formula to find the roots. The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the roots can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our case, a = 4, b = -12, and c = 9. Now, let's substitute these values into the quadratic formula to find the roots.
x = (-(-12) ± √((-12)^2 - 4 * 4 * 9)) / (2 * 4)
x = (12 ± √(144 - 144)) / 8
x = (12 ± √0) / 8
Since the discriminant (√(b^2 - 4ac)) in the quadratic formula is zero, this means that the square root of 0 is 0. Therefore, we can simplify the equation further:
x = 12 / 8
x = 1.5
So, the only root of the equation 4x^2 + 9 = 12x is x = 1.5.