Which two values of x are roots of the polynomial below x^2-11x+17

Answer

9.14   and 1.86

Explanation

x²-11x+17

The first thing is to equate it to zero.

x²-11x+17 = 0

x²-11x = -17

x² - 11x + (11/2)² = -17 + (11/2)²

(x² - 11/2)² = -17 + 121/4

(x - 11/2)² = 13.25

x -11/2 = √13.25                            or      x - 11/2 = -√13.25

x = √13.25 + 11/2                                            x = -√13.25 + 11/2

   = 3.64 + 5.5                                                     = -3.64 + 5.5

   = 9.14                                                              = 1.86

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

hello from mrbilldoesmath!

answer:   x (x+6)^2, choice b

discussion:

factor x out of the equation:

x^3 + 12x^2 + 36x = x (x^2 + 12x + 36).

note that 6+6 = 12 and 6*6 = 36 so the above factors into:

x (x+6)^2

which is choice b

you,

mrb