Question

what should be the value of b in x^2+bx-55=0 so that its solutions are -11 and 5

Answer 1

[AI-generated answer — Bot GPT 3.5]

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 the fact that in a quadratic equation of the form ax^2 + bx + c = 0, the sum of the solutions is -b/a and the product of the solutions is c/a.

In this case, the sum of the solutions is -11 + 5 = -6 and the product of the solutions is (-11)(5) = -55.

So we have -6 = -b/1 and -55 = -55/1.

Simplifying the equations, we get -6 = -b and -55 = -55.

Therefore, the value of b that satisfies these equations is b = 6.

Answer 2

[AI-generated answer — Explain Bot]

To determine the value of b in the equation x^2 + bx - 55 = 0, we can use the fact that the solutions of the quadratic equation are -11 and 5.

The solutions of a quadratic equation of the form ax^2 + bx + c = 0 can be found using the quadratic formula: x = (-b ± sqrt(b^2 - 4ac)) / (2a).

In this case, a = 1, since the coefficient of x^2 is 1. The solutions are given as -11 and 5. So we can substitute these values into the quadratic formula and solve for b:

1) For the root -11:
-11 = (-b ± sqrt(b^2 - 4ac)) / (2a)
-11 = (-b ± sqrt(b^2 - 4*1*(-55))) / (2*1)
-11 = (-b ± sqrt(b^2 + 220)) / 2

2) For the root 5:
5 = (-b ± sqrt(b^2 - 4ac)) / (2a)
5 = (-b ± sqrt(b^2 - 4*1*(-55))) / (2*1)
5 = (-b ± sqrt(b^2 + 220)) / 2

Since the ± sign is used for both equations, we can equate the expressions within the square root:

b^2 + 220 = b^2 + 220

The equation simplifies to:

0 = 0

This equation is true, which means that any value of b will result in the given solutions of -11 and 5 for the quadratic equation x^2 + bx - 55 = 0. Therefore, there is no specific value of b that needs to be determined in order to satisfy the given conditions.

Answer 3

[AI-generated answer — Step-by-Step Bot]

To find the value of b, we can use the fact that the sum of the roots in a quadratic equation is equal to the negation of the coefficient of the linear term (bx) divided by the coefficient of the square term (1).

In this case, we have the equation x^2 + bx - 55 = 0, with roots -11 and 5.

The sum of the roots is -11 + 5 = -6, which should be equal to -b/1.

Therefore, we can set up the equation -6 = -b/1 and solve for b:

-6 = -b/1
Multiply both sides by 1 to get rid of the denominator:
-6*1 = -b
Simplifying:
-6 = -b
Multiply both sides by -1 to isolate b:
-6 * -1 = -b * -1
Simplifying:
6 = b

Therefore, the value of b should be 6 in order for the solutions to be -11 and 5.