How many x-incercepts appear on the graph of this polynomial function f(x)=x^4-5x^2

Step-by-step explanation:

How many x-intercepts?

Factoring this polynomial eases the job of counting the intercepts.

f(x)=x^4-5x^2 = x^2(x^2 - 5)

Setting x^2 = 0 leads to two x-intercepts:  (0, 0) and (0, 0) (a double root).

Setting x^2 - 5 = 0 yields the intercepts (-√5, 0) and (√5, 0).

Thus, there are, strictly speaking, FOUR x-intercepts.  Of these, three are immediately visible.

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

answer: the value of x is 7cm

step-by-step explanation: