Consider the following statements: 1. If $x$ be real, then $- \frac{9}{2} \leq \frac{3x - 4}{x^{2} + 1} \leq \frac{1}{2}$ 2. If $x$ is real, then the greatest value of $\frac{x^{2} + 14x + 9}{x^{2} + 2x + 3}\$is 4 3. If $ax^{2} + bx + c = 0;a
eq 0,a,b,c \in R$ has no real roots, then $(a + b + c)c 0$ Which of these is/ are correct?

Question

Consider the following statements: 1. If $x$ be real, then $- \frac{9}{2} \leq \frac{3x - 4}{x^{2} + 1} \leq \frac{1}{2}$ 2. If $x$ is real, then the greatest value of $\frac{x^{2} + 14x + 9}{x^{2} + 2x + 3}\$is 4 3. If $ax^{2} + bx + c = 0;a 
eq 0,a,b,c \in R$ has no real roots, then $(a + b + c)c > 0$ Which of these is/ are correct?

Dr. Abubacker · Accepted Answer

The correct answer is Option D: All of these.

Explanation

Reviewed by Dr. Abubacker

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