What should be the value of b in x2+bx−55=0

Question

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

−6
negative 6

−16
negative 16

6
6

16

Answer 1

To determine 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, for the quadratic equation \( ax^2 + bx + c = 0 \):

1. The sum of the roots (solutions) is given by \( -\frac{b}{a} \).
2. The product of the roots is given by \( \frac{c}{a} \).

In this case:

• The roots are \( r_1 = -11 \) and \( r_2 = 5 \).
• The product of the roots \( r_1 \times r_2 = (-11) \times (5) = -55 \), which matches with the constant term of the equation since \( c = -55 \).
• The sum of the roots \( r_1 + r_2 = -11 + 5 = -6 \).

Using the relationship for the sum of the roots: \[ -\frac{b}{1} = -6 \implies b = 6 \]

Thus, the value of \( b \) should be \( 6 \).

The correct response is: 6