Consider a quadratic equation of the form x + bx+c0, where b and c are rational numbers, Fill in the blanks in the following proof that if one solution is rational, then the other solution is also rational. Proof: Supposex+bx+c=0 is any quadratic equation where b and care rational numbers, and suppose one solution ris rational. Call the other solutions. Then x²+bx+c= (x-rx-s), Multiply out (x-r)(x-a) and set it equal to x²+bx+c to obtain x²+bx+c=x² + -r+s ✔are rational and solve for a in terms of b and r to obtain a conclude that b-r is rational, and so sis rational. Since and r 4 Fouate coeft X and since differences of rational numbers are rational, we PS
Consider a quadratic equation of the form x + bx+c0, where b and c are rational numbers, Fill in the blanks in the following proof that if one solution is rational, then the other solution is also rational. Proof: Supposex+bx+c=0 is any quadratic equation where b and care rational numbers, and suppose one solution ris rational. Call the other solutions. Then x²+bx+c= (x-rx-s), Multiply out (x-r)(x-a) and set it equal to x²+bx+c to obtain x²+bx+c=x² + -r+s ✔are rational and solve for a in terms of b and r to obtain a conclude that b-r is rational, and so sis rational. Since and r 4 Fouate coeft X and since differences of rational numbers are rational, we PS
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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Transcribed Image Text:Consider a quadratic equation of the form x+bx+c 0, where b and c are rational numbers, Fill in the blanks in the following proof that if one solution is rational, then the other
solution is also rational.
Proof: Supposex+bx+c=0 is any quadratic equation where b and care rational numbers, and suppose one solution ris rational. Call the other solutions. Then
x²+bx+c= (x-rx-s), Multiply out (x-r)(x-a) and set it equal to x² + bx+c to obtain x² bx+c=x² +
-r+s
Since and r
✔are rational
and solve for a in terms of b and r to obtain a
conclude that b-r
is rational, and so sis rational.
4
Fosate coeft
X
and since differences of rational numbers are rational, we
PS
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