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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
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.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 2 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
