DISCOVER ■ PROVE: Relationship Between Solutions and Coefficients The Quadratic Formula gives us the solutions of a
- (a) Find the solutions of the equation x2 − 9x + 20 = 0, and show that the product of the solutions is the constant term 20 and the sum of the solutions is 9, the negative of the coefficient of x.
- (b) Show that the same relationship between solutions and coefficients holds for the following equations:
- (c) Use the Quadratic Formula to prove that in general, if the equation x2 + bx + c = 0 has solutions r1, and r2, then c = r1r2 and b = −(r1 + r2).
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