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xz_007 [3.2K]
3 years ago
9

Which of the following is the converse of the statement "if it is snowing, then it is my Birthday?

Mathematics
2 answers:
k0ka [10]3 years ago
8 0
That would be "If it is my birthday, then it is snowing."

Hope this helps!

- Juju
Andreas93 [3]3 years ago
6 0
If it is my birthday, then it is snowing
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If a polynomial has one root in the form a+√b , it has a second root in the form of a_√b
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When roots of polynomials occur in radical form, they occur as two conjugates.
That is,
The conjugate of (a + √b) is (a - √b) and vice versa.
To show that the given conjugates come from a polynomial, we should create the polynomial from the given factors.

The first factor is x - (a + √b).
The second factor is x - (a - √b).

The polynomial is
f(x) = [x - (a + √b)]*[x - (a - √b)]
      = x² - x(a - √b) - x(a + √b) + (a + √b)(a - √b)
      = x² - 2ax + x√b - x√b + a² - b
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This is a quadratic polynomial, as expected.

If you solve the quadratic equation x² - 2ax + a² - b = 0 with the quadratic formula, it should yield the pair of conjugate radical roots.
x = (1/2) [ 2a +/- √(4a² - 4(a² - b)]
   = a +/- (1/2)*√(4b)
   = a +/- √b
x = a + √b, or x = a - √b, as expected.
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a is the answer

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