Question

If x is real, then the maximum and minimum values of expression $\frac{x^{2} + 14x + 9}{x^{2} + 2x + 3}$ will be-

• A. 4, – 5
• B. 5, – 4
• C. – 4, 5
• D. – 4, – 5

Answer 1

Answer: (A)

4, – 5

Answer 2

y = $\frac{x^{2} + 14x + 9}{x^{2} + 2x + 3}$

x²(y–1) + 2x(y – 7) + 3(y – 3) = 0

x Ī R , D ³ 0

4 [(y – 7)² – 3(y – 1) (y–3)] ³ 0

[y² + 49 – 14y – 3y² – 9 + 12y] ³ 0

2y² + 2y – 40 £ 0 Ž y² + y – 20 £ 0

(y + 5) (y – 4) £ 0 Ž y Ī [–5,4]

Min. = – 5, Max. = 4