Given the roots of a quadratic equation, we can find the equation by using the fact that the product of the roots equals to the constant term (c) divided by the coefficient of the quadratic term (a) and the sum of the roots equals to the opposite of the coefficient of the linear term (b) divided by the coefficient of the quadratic term (a).
The general form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants, and x is the variable.
Given that the roots of the equation are -6 and 1, we can find the equation as follows:
The product of the roots is -6 * 1 = -6
The sum of the roots is -6 + 1 = -5
We know that:
c / a = product of roots and
-b / a = sum of roots
So we can form the equation as:
ax^2 + bx + c = 0
ax^2 + (-5)x + (-6) = 0
So the quadratic equation whose roots are -6 and 1 is
ax^2 - 5x - 6 = 0
We can also verify that the roots of this equation are -6 and 1 by factoring or using the quadratic formula.