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1.5.1. (a) Show, that if x₁ and 2 are two solutions of a quadratic equation ax² + bx + c = 0 (with b a 0), then x₁1 + X2 = −− (these are often called Vieta's Formulas). Also, find a a formula for x + x2 in terms of a, b and c. and x₁ x2 = с a (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.

1.5.1. (a) Show, that if x₁ and 2 are two solutions of a quadratic equation ax² + bx + c = 0 (with b a 0), then x₁1 + X2 = −− (these are often called Vieta's Formulas). Also, find a a formula for x + x2 in terms of a, b and c. and x₁ x2 = с a (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.

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 2 are two solutions of a quadratic equation ax² + bx + c = 0 (with b с a 0), then x1 + x2 = −; and x₁ x2 = (these are often called Vieta's Formulas). Also, find a a a formula for x² + x² 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 2 are two solutions of a quadratic equation ax² + bx + c = 0 (with b с a 0), then x1 + x2 = −; and x₁ x2 = (these are often called Vieta's Formulas). Also, find a a a formula for x² + x² 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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