Write a quadratic equation whose roots are 3 and -6 and leading coefficient is 1. Please help
recall that if a is a root, then (x-a) is a factor of f(x). So, you have
(x-3)(x+6) = 0
Naaa Ms. Sue really, we couldn't tell.
To write a quadratic equation with given roots, we can use the factored form of a quadratic equation: (x - r1)(x - r2) = 0, where r1 and r2 are the roots.
Given that the roots are 3 and -6, we can substitute these values into the equation.
So, our equation becomes: (x - 3)(x - (-6)) = 0
Simplifying, we get: (x - 3)(x + 6) = 0
Expanding the equation further: x^2 + 6x - 3x - 18 = 0
Combining like terms, we finally get the quadratic equation: x^2 + 3x - 18 = 0
Thus, the quadratic equation with roots 3 and -6 and a leading coefficient of 1 is x^2 + 3x - 18 = 0