If the two equations 3x^2+ax+1=0 and 2x^2+bx+1 have a common real root, find a and b.

Asked by aahnik.mohanty | 11th Jun, 2019, 08:02: PM

Expert Answer:

3 straight x squared plus ax plus 1 equals 0
2 straight x squared plus bx plus 1 equals 0
For space common space root space condition space is
fraction numerator straight x squared over denominator straight a minus straight b end fraction equals fraction numerator negative straight x over denominator 3 minus 2 end fraction equals fraction numerator 1 over denominator 3 straight b minus 2 straight a end fraction
so space we space have
fraction numerator straight x squared over denominator straight a minus straight b end fraction equals fraction numerator negative straight x over denominator 3 minus 2 end fraction
fraction numerator straight x squared over denominator straight a minus straight b end fraction equals negative straight x
straight x equals straight b minus straight a
so space we space get space the space condition space that space the space common space root space should space be space equal space to space straight b minus straight a
to space get space the space values space of space straight a space and space straight b space additional space information space is space required.

Answered by Arun | 13th Jun, 2019, 09:38: AM