Question

If x^2-ax+b and x^2-cx+d both have a factor x-m prove that m=d-b/c-a

Answer 1

see explanation

Explanation:

Given (x - m) is a factor of both then x = m make both expressions equal to zero.

m² - am + b = 0

m² - cm + d = 0

Then

m² - am + b = m² - cm + d ( subtract m² - cm from both sides )

cm - am + b = d ( subtract b from both sides )

cm - am = d - b ← factor out m from each term on the left side

m(c - a) = d - b ← divide both sides by (c - a)

m =
`(d-b)/(c-a)` ← as required