Me
how many and what type of solution(s) does the equation have?
4p^2=12p-5

a. 1 rational solution
b. 2 irrational solutions
c. 2 non-real solutions
d. 2 rational solutions

  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.

the answer is:

the answer is:

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

then, calculating we have:

hence, the answer is:

have a nice day!

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step-by-step explanation: