Write a quadratic equation with the given roots. Write the equation in the form ax^2+bx+c=0 , where a, b, and c are integers. –7 and –2

Accepted Solution

Answer:   x² +9x +14 = 0Step-by-step explanation:Since the roots are integers, we can write the equation in the given form using a=1. Then b is the opposite of the sum of the roots:   b = -((-7) +(-2)) = 9And c is the product of the roots:   c = (-7)(-2) = 14So, the desired quadratic equation is ...   x² +9x +14 = 0_____The attached graph confirms the roots of this equation._____Another wayFor root r, a factor of the equation is (x -r). For the given two roots, the factors are ...   (x -(-7))(x -(-2)) = (x +7)(x +2)When expanded, this expression is ...   x(x +2) +7(x +2) = x² +2x +7x +14   = x² +9x +14We want the equation where this is set to zero:   x² +9x +14 = 0___If a root is a fraction, say p/q, then the factor (x -p/q) can also be written as (qx -p). In this case, expanding the product of binomial factors will result in a value for "a" that is not 1.