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

Responses

16
16

−16
negative 16

6
6

−6

1 answer

To find the value of b in the quadratic equation x2+bx55=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 x2+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=6b=6

  2. The product of the roots: 11×5=55 This confirms our constant term is correct since the quadratic is x2+bx55=0.

Thus, the value of b is 6.

The correct response is: 6

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