What should be the value of b in x^2+bx−55=0

Question

so that its solutions are −11
and 5? (1 point)
Responses

6
6

−16
negative 16

16
16

−6

Answer 1

To find the value of \( b \) in the quadratic equation \( x^2 + bx - 55 = 0 \) such that the solutions are \( -11 \) and \( 5 \), we can use Vieta's formulas. According to Vieta's formulas:

1. The sum of the roots (\( r_1 + r_2 \)) is equal to \(-b\).
2. The product of the roots (\( r_1 \cdot r_2 \)) is equal to the constant term divided by the coefficient of \( x^2 \).

Given the roots \( -11 \) and \( 5 \):

1. Sum of the roots: \[ -11 + 5 = -6 \] Therefore, \(-b = -6\) which gives: \[ b = 6 \]

2. Product of the roots: \[ (-11) \cdot 5 = -55 \] This confirms that the product matches since \(-55\) is the constant term.

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

The correct response is: 6