Question

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

Answer 1

To find the value of \( b \) in the quadratic equation \( x^2 + bx - 55 = 0 \) such that its solutions are \( -11 \) and \( 5 \), we can use the fact that if \( p \) and \( q \) are the roots of the quadratic equation \( ax^2 + bx + c = 0 \), then:

1. The sum of the roots \( p + q = -\frac{b}{a} \).
2. The product of the roots \( pq = \frac{c}{a} \).

In our case, the specific values are:
- \( p = -11 \)
- \( q = 5 \)
- \( a = 1 \)
- \( c = -55 \)

First, calculate the sum of the roots:
\[
p + q = -11 + 5 = -6
\]
According to the formula for the sum of the roots, we have:
\[
-6 = -b \quad \Rightarrow \quad b = 6
\]

Next, calculate the product of the roots:
\[
pq = (-11)(5) = -55
\]
According to the formula for the product of the roots, we have:
\[
-55 = -55
\]
This confirms the values we derived.

Thus, the value of \( b \) is \( 6 \).

So the answer is \( \boxed{6} \).