Question

If two equations x^2 + cx + ab = 0 and x^2 + bx + ca = 0 have a common root, then show that a + b
+ c = 0.
Can anyone EXPLAIN this answer please?? I need it now ​

Answer 1

x² + cx + ab = 0 ; x² + bx + ca = 0

The condition for only one root common is

$(c_{1}a_{2} - c_{2}a_{1}) {}^{2} = (b_{1}c_{2} - b_{2}c_{1})(a_{1}b_{2} - a_{2}b_{1})$

[ab - ca]² = [ac² - ab²][b - c]

a²b² + a²c² - 2a²bc = abc² - ac³ - ab³ + ab²c

ac³ + ab³ + a²b² + a²c² = 2a²bc + ab²c + abc²

c³ + b³ + ab² + ac² = 2abc + b²c + bc²