Solving Quadratic Equations Using Patterns Quick Check

Question

3 of 53 of 5 Items
Question
What should be the value of b in x2+bx−55=0 so that its solutions are −11 and 5? (1 point)
Responses

−16
negative 16

16
16

−6
negative 6

6
6
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Answer 1

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

1. The sum of the roots is equal to \( -b \).
2. The product of the roots is equal to \( c \).

Here, the solutions are \( -11 \) and \( 5 \).

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

2. Product of the roots: \[ -11 \times 5 = -55 \] This supports that the value for \( c \) is indeed \(-55\).

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

The correct response is: 6.