Question

If 'x' is real than the maximum and minimum value of expression $\frac{x^{2} + 14x + 9}{x^{2} + 2x + 3}$ is

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

Answer 1

Answer: (A)

4, –5

Answer 2

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

Ž x²(1 – y) + 2x(7 – y) + 9 – 3y = 0

for 'x' to be real D ³ 0

4.(7 – y)² – 4.(1 – y)(9 – 3y) ³ 0

49 + y² – 14y – (9 – 3y – 9y + 3y²) ³ 0

–2y² – 2y + 40 ³ 0

Ž y² + y – 20 £ 0

(y + 5)(y – 4) £ 0

+ – +

–5 4

–5 £ y £ 4