The product of the roots of the equation (x−4)(x−2)+(x−2)(x−6)=0 is
A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.
Solution
Since the two terms have a common factor, then we factor and obtain (x−2)((x−4)+(x−6))=0. This gives (x−2)(2x−10)=0. Therefore, x−2=0 (which gives x=2) or 2x−10=0 (which gives x=5). Therefore, the two roots of the equation are x=2 and x=5. Their product is 10.
Want a route through all this instead of an archive? The track
puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.
Source: Omni-MATH,
licensed Apache-2.0.
Statement reproduced verbatim; metadata (topic, difficulty) added by this project.