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13 May, 03:52

Using the discriminant, how many solutions and what type of solution (s) does 3p-9p^2=6 have?

a. 2; irrational

b. 2; rational

c. 1; rational

d. no real solutions

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  1. 13 May, 07:12
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    d. no real solutions

    Step-by-step explanation:

    3p - 9p² = 6

    0 = 9p² - 3p + 6

    0 = 3p² - p + 2

    The discriminant of ax² + bx + c is b² - 4ac.

    If the discriminant is negative, there are no real roots.

    If the discriminant is zero, there is 1 real root.

    If the discriminant is positive, there are 2 real roots.

    If the discriminant is a perfect square, the root (s) are rational.

    If the discriminant isn't a perfect square, the root (s) are irrational.

    Finding the discriminant:

    a = 3, b = - 1, c = 2

    (-1) ² - 4 (3) (2) = - 23

    The discriminant is negative, so there are no real roots.
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