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
negative 16

−6
negative 6

16
16

6
6

Answer 1

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, for a quadratic equation of the form \( x^2 + px + q = 0 \):

• The sum of the roots \( r_1 + r_2 = -p \)
• The product of the roots \( r_1 \cdot r_2 = q \)

Here, the roots are \( r_1 = -11 \) and \( r_2 = 5 \).

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

2. Product of the roots: \[ (-11)(5) = -55 \] This confirms that \( q = -55 \) is correct.

Since both conditions are satisfied, the value of \( b \) should be \( 6 \).

The correct answer is:

6