Based on an experiment I just did, it gets an A in Algebra I: Q. What are the roots of the equation x^2 - x - 6 = 0 A. To find the roots of the equation x^2 -

Based on an experiment I just did, it gets an A in Algebra I: Q. What are the roots of the equation x^2 - x - 6 = 0 A. To find the roots of the equation x^2 - x - 6 = 0, we can use the quadratic formula: x = (-b ± sqrt(b^2 - 4ac)) / 2a where a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c = 0. In this case, a = 1, b = -1, and c = -6. Substituting these values into the formula, we get: x = (-(-1) ± sqrt((-1)^2 - 4(1)(-6))) / 2(1) x = (1 ± sqrt(1 + 24)) / 2 x = (1 ± sqrt(25)) / 2 Simplifying, we get: x1 = (1 + 5) / 2 = 3 x2 = (1 - 5) / 2 = -2 Therefore, the roots of the equation x^2 - x - 6 = 0 are x = 3 and x = -2. Q. Could you solve it more easily by factoring the polynomial? A. Yes, you can also solve the equation x^2 - x - 6 = 0 by factoring the polynomial. To do this, we need to find two numbers whose product is -6 and whose sum is -1, which are -3 and 2. Then, we can rewrite the polynomial as: x^2 - x - 6 = (x - 3)(x + 2) = 0 Using the zero product property, we know that either (x - 3) = 0 or (x + 2) = 0. Therefore, the roots of the equation are x = 3 and x = -2, which are the same values we obtained using the quadratic formula. So, the factored form of the polynomial is (x - 3)(x + 2) = 0, and its roots are x = 3 and x = -2.