determine the quadratic equation with x-3 sqrt of 2 and -3 sqrt 2 in the form ax^2+bx+c=0?? How do you do this I do not know how to..please explain
Thanks!
To determine the quadratic equation with given roots, x = 3√2 and x = -3√2, we can use the fact that if a quadratic equation has roots α and β, then the equation can be expressed in the form:
(x - α)(x - β) = 0
In this case, the roots are x = 3√2 and x = -3√2, so the equation becomes:
(x - 3√2)(x - (-3√2)) = 0
Simplifying this expression, we have:
(x - 3√2)(x + 3√2) = 0
Expanding the equation further, using the FOIL method (First, Outer, Inner, Last), we get:
x^2 - 3√2x + 3√2x - 18 = 0
As the middle terms, -3√2x and 3√2x, cancel each other out, the equation simplifies to:
x^2 - 18 = 0
So, the quadratic equation in the required form is:
x^2 - 18 = 0
In this equation, a = 1, b = 0, and c = -18.