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

Question

Responses

16
16

−16
negative 16

6
6

−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 Vieta's formulas, which state that for a quadratic equation of the form \( x^2 + px + q = 0 \):

1. The sum of the roots (solutions) is equal to \( -p \).
2. The product of the roots is equal to \( q \).

In this case, the roots are \( -11 \) and \( 5 \).

1. The sum of the roots: \[ -11 + 5 = -6 \] According to Vieta's formulas, this sum is equal to \( -b \). Therefore: \[ -b = -6 \implies b = 6 \]

2. The product of the roots: \[ -11 \times 5 = -55 \] This confirms our constant term is correct since the quadratic is \( x^2 + bx - 55 = 0 \).

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

The correct response is: 6