[JEE Main 2006] if x is real the maximum value of 3x 2 9x 17 3x 2
If $x$ is real, the maximum value of $\dfrac{3x^2+9x+17}{3x^2+9x+7}$ is
(a) $\frac14$
(b) $41$
(c) $1$
(d) $\frac{17}7$
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 2d ago
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Correct answer: (b) $41$
Let $t=3x^2+9x\ge-\frac{27}4$; the expression $=1+\frac{10}{t+7}$ is largest when $t+7=\frac14$, giving $1+40=41$.
JEE Main 2006 · Quadratic Equations and Inequations — verified solution by the Vidaara Team.
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