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: $$-b=-6⟹b=6$$

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