What should be the value of b in x2+bx−55=0 so that its solutions are −11 and 5? (1 point)

Question

Responses

6
6

16
16

−6
negative 6

−16

Answer 1

To find the value of \( b \) in the equation \( x^2 + bx - 55 = 0 \) given 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 \( -\frac{b}{a} \).
2. The product of the roots is equal to \( \frac{c}{a} \).

In this case, we have:

• The sum of the roots: \( -11 + 5 = -6 \)
• The product of the roots: \( -11 \cdot 5 = -55 \)

Since \( a = 1 \) and \( c = -55 \), we can set up the equation for the sum of the roots:

\[ -(-6) = -\frac{b}{1} \]

This gives us:

\[ -6 = -b \quad \Rightarrow \quad b = 6 \]

Thus, the value of \( b \) that satisfies the condition is:

6