Given: \(\displaystyle{a}{x}^{{{2}}}+{b}{x}+{c}={0}\), with a,b and c being whole

alparcero97oy

alparcero97oy

Answered question

2022-03-27

Given:
ax2+bx+c=0, with a,b and c being whole numbers, and this equation having two solutions. The solutions of such an equation are sometimes rational, but mostly not. How do you prove that the sum of the solutions x1+x2 and the product x1x2 are always rational?

Answer & Explanation

Drake Huang

Drake Huang

Beginner2022-03-28Added 15 answers

Use the formula:
x=b±b24ac2a,
from which it follows that
x1+x2=ba,x1x2=ca.
These are called Vieta's formulas and can be generalised to polynomials of arbitrary degree.

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