Question

Q.1 find 'a' if the equations x²-(a +2)x + 3a =0
and x² - (a +3)x + 5a =0 has a common root​

Answer 1

Answer:

If b is a common root then b^2+2b+3a=0 and 2b^2+3b+5a=0. From the above

2(-2b-3a)+3b+5a=0 or (-b) -a=0, i.e. b=(-a). Putting in the first equation (a^2) -2a+3a=0 or a^2+a=0, i.e. a =0 or (-1). Now a=0 implies that the common root b=(-0)=0. Therefore a =(-1)

Check “Resultant” in Wikipedia