Find the number of possible positive real zeros of f(x)=8x^4-72x^3+144x^2 a. four c. two or none b. three d. none select the best answer from the choices provided a b c d

  c.  two or none

Step-by-step explanation:

The signs of the coefficients are ...

  + - +

so there are two sign changes: + to -, and - to +. Descartes' rule of signs tells you to interpret this to mean there are 2 or 0 possible positive real roots.

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Pairs of roots are possibly complex, so the number of sign changes can be reduced by any even number to take that possibility into account. That is why 2 sign changes can mean either 2 or 0 positive real roots.

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A graph shows there to be 2 positive real roots and a root at x=0 with multiplicity 2. The latter should be no surprise, since x^2 is a factor of f(x).

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15