Answer:
D. 2 rational solutions
Step-by-step explanation:
You can answer this question by (a) solving the equation, or (b) evaluating the discriminant.
In the latter case, ...
4p^2 -12p +5 = 0 . . . . . . a=4, b=-12, c=5
The discriminant is ...
b^2 -4ac = (-12)^2 -(4)(4)(5) = 64
This is a perfect square, so the roots are real and rational, choice D.
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Once you get the quadratic in the standard form above, you can see that the factors will be related to the factors of 20 that sum to -12. As soon as you find these integer factors of 20, you know the roots are rational.
4p^2 -10p -2p +5 = 0 . . . . . . rewrite -12p using the factors -10 and -2
2p(2p -5) -1(2p -5) = 0 . . . . . .factor by grouping
(2p -1)(2p -5) = 0
The solutions are the values of p that make the factors zero, 1/2 and 5/2. Both are rational numbers.
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A graphing calculator shows you very quickly that the two roots are rational.
