Question

Let a, b be the roots of x² + (3 – l)x – l = 0. The value of l for which a² + b² is minimum, is -

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

Answer: (C)

2

Answer 2

a + b = l – 3 ; ab = – l

a² + b² = (a + b)² – 2 ab = (l – 3)² + 2l

= l² – 6l + 2l + 9 = l² – 4l + 9

( l = $\left( –\frac{b}{2a} \right)$ Ž l Ž l = 2 )

y_min = $–\frac{D}{4a}$ = $\frac{–(16–36)}{4}$ = 5 ; at l = 2, y_min = 5