Q. If at least one root of $2x^{2} + 3x + 5 = 0\ and\ ax^{2} + bx + c = 0,\ a,\ b,\ c \in N$ is common, then the maximum value of $a + b + c$ is
A) 10
B) 0
C) Does not exist
D) None of these
Explanation
(c)
Roots of the equation $2x^{2} + 3x + 5 = 0$ are
$x = \frac{- 3 \pm \sqrt{9 - 40}}{6}$ (imaginary roots)
Hence, both roots coincide, so on comparing
$\frac{a}{2} = \frac{b}{3} = \frac{c}{5} = k$
$\Rightarrow a = 2k,\ b = 3k,\ c = 5k$
$\Rightarrow a + b + c = 10k$
So, maximum value does not exist.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.