Question

What should be the value of b in x ^ 2 + bx - 55 = 0 so that its solutions are -11 and 5? 6 16 -6 -16

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the value of b, we can use the fact that the sum of the solutions of a quadratic equation in the form of ax^2 + bx + c = 0 is equal to -b/a, and the product of the solutions is equal to c/a.

Given that the solutions are -11 and 5, the sum of the solutions is -11 + 5 = -6. This means that -b/a = -6.

Also, the product of the solutions is -11 * 5 = -55. This means that c/a = -55.

We can solve these two equations simultaneously to find the value of b.

-b/a = -6
c/a = -55

Rearranging the first equation, we have:
b/a = 6

Multiplying both sides of the second equation by a, we get:
c = -55a

Since c = -55, we have:
-55 = -55a
a = 1

Substituting this value of a into b/a = 6, we can find b:
b/1 = 6
b = 6

Therefore, the value of b in the quadratic equation x^2 + bx - 55 = 0, whose solutions are -11 and 5, is 6.

Answer 2

Solve the following quadratic equation using the perfect square trinomial pattern : x ^ 2 - 16x + 64; x = - 64; x = 8; x = 64; x = - 8

Answer 3

[AI-generated answer — Bot GPT 3.5]

We can solve the quadratic equation x^2 - 16x + 64 = 0 using the perfect square trinomial pattern, which is a^2 - 2ab + b^2 = (a - b)^2.

In this case, the perfect square trinomial pattern can be applied as (x - 8)^2 = 0.

If (x - 8)^2 = 0, it means that x - 8 = 0.

Adding 8 to both sides of the equation, we get:
x = 8

Therefore, the solution to the quadratic equation x^2 - 16x + 64 = 0 is x = 8.

Answer 4

Gabriel was asked to solve x ^ 2 - 36 = 0 by factoring using the difference of squares pattern. What isare the correct solution (s) ? (point) x = 6x = - 6; x=18.x=-18; x = 6; x = - 6

Answer 5

[AI-generated answer — Bot GPT 3.5]

To solve the quadratic equation x^2 - 36 = 0 using the difference of squares pattern, we can rewrite it as (x)^2 - (6)^2 = 0.

This expression can be factored as (x + 6)(x - 6) = 0.

Now we can set each factor equal to zero and solve for x:

Setting x + 6 = 0:
x = -6

Setting x - 6 = 0:
x = 6

Therefore, the correct solutions to the quadratic equation x^2 - 36 = 0 using the difference of squares pattern are x = -6 and x = 6.

Answer 6

[AI-generated answer — Explain Bot]

To find the value of b in the quadratic equation x^2 + bx - 55 = 0, we can use the fact that the sum and product of the solutions of a quadratic equation can be determined from the coefficients.

The sum of the solutions (root or zeros) of a quadratic equation is equal to the negation of the coefficient of the linear term (b), divided by the coefficient of the quadratic term (1 in this case). So, we have:

Sum of solutions = -b/1 = -b.

Since we are given that the solutions are -11 and 5, we can find the sum of the solutions:

Sum of solutions = -11 + 5 = -6.

Therefore, we have:

-b = -6.

Solving for b, we multiply both sides by -1:

b = 6.

So, the value of b that makes the solutions of the quadratic equation x^2 + bx - 55 = 0 equal to -11 and 5 is 6.