What should be the value of b in x^2+bx-55=0 so that its solutions are -11 and 5

Question

What should be the value of b in x^2+bx-55=0 so that its solutions are -11 and 5
A. -16
B. 6
C. -6
D. 16

GPT-4o mini · Answer

To find the value of $ b $ in the equation $ x^2 + bx - 55 = 0 $ such that its solutions are $ -11 $ and $ 5 $, we can use Vieta's formulas. According to Vieta's formulas: 1. The sum of the roots (solutions) is equal to $ -b $. 2. The product of the roots is equal to the constant term. Given the roots $ -11 $ and $ 5 $: 1. **Sum of the roots**: $$ -11 + 5 = -6 $$ Therefore, we know: $$ -b = -6 \implies b = 6 $$ 2. **Product of the roots**: $$ (-11) \times 5 = -55 $$ This confirms the constant term is correct since $ -55 $ matches the equation $ x^2 + bx - 55 = 0 $. Thus, the correct value of $ b $ is $ 6 $. The answer is $ \boxed{6} $.