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a + 0), then x1 + x2 = -- and x1· x2 = (these are often called Vieta's Formulas). Also, find a a a formula for x + x, in terms of a, b and c. Use Part (a) to find a quadratic equation with two distinct real solutions, given that the sum of the solutions is 47 and their product –59 .

a + 0), then x1 + x2 = -- and x1· x2 = (these are often called Vieta's Formulas). Also, find a a a formula for x + x, in terms of a, b and c. Use Part (a) to find a quadratic equation with two distinct real solutions, given that the sum of the solutions is 47 and their product –59 .

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1.5.1. (a) Show, that if x1 and x2 are two solutions of a quadratic equation ax? + bx + c = 0 (with a + 0), then xi + x2 and x1· X2 (these are often called Vieta's Formulas). Also, find a a а formula for x + x, in terms of a, b and c. (b) Use Part (a) to find a quadratic equation with two distinct real solutions, given that the sum of the solutions is 47 and their product -59 .
Transcribed Image Text:1.5.1. (a) Show, that if x1 and x2 are two solutions of a quadratic equation ax? + bx + c = 0 (with a + 0), then xi + x2 and x1· X2 (these are often called Vieta's Formulas). Also, find a a а formula for x + x, in terms of a, b and c. (b) Use Part (a) to find a quadratic equation with two distinct real solutions, given that the sum of the solutions is 47 and their product -59 .
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