The roots of a polynomial equation are the values of x that you can plug in so the function is equal to 0. To find the roots, you would want to factor the polynomial and set the factored form equal to zero.
1) First factor the polynomial. The factored form of is (x + a)(x + b), where a and b are two numbers that multiply to -72 and add up to 1. By testing numbers that are factors of -72, you can find that 8 x 9 = 72, meaning that either 8 or 9 has to be negative to get -72. But which one of those is negative?
Since you want the two numbers to add up to 1, that means 9 must be positive and 8 must be negative, since -8 + 9 = 1! That makes a and b, 9 and -8. Your factored form would be (x - 8)(x + 9) = 0.
2) Now you want to find values of x where the function is equal to 0. Remember that anything multiplied by 0 is equal to zero. That means you can set each factor, (x - 8) and (x + 9), equal to 0 to find the two values of x (aka the roots)! Factor 1:x - 8 = 0x = 8 Factor 2:x + 9 = 0x = -9 Your two roots are 8 and -9. -------- Answer: 8 and -9
