Question

If equations $a{x}^2+bx+c=0and{x}^2+3x+4=0$ has common roots then possible value of (a,b,c) taken in order is (a,b,c).

Answer 1

Given equation are

$a{x}^2+bx+c=0$

and $x^2+3x+4=0$

$D=b^2-4ac$

$=9-4\times 4\times 1$

$=-7$

$X<0$

roots are imaginary and imaginary roots always exists in paris (conjugate)

$\therefore$ $a{x}^2+bx+c=0$ and $x^2+3x+4=0$ are identical

$\therefore$ $\frac{a}{1}=\frac{b}{3}=\frac{c}{4}$

$\therefore$ $(a,b,c)=(1,3,4)$