What are the possible numbers of positive real, negative real, and complex zeros of f(x) = 8x4 + 13x3 − 11x2 + x + 9?

Positive real zeros- 2 or 0

Negative real zeros - 2 or 0

Complex zeros-4 or 2 or 0

Step-by-step explanation:

Given: A fourth degree polynomial is arranged in descending order already .

We can see that it has two sign change from second to third term and then third to fourth ,so by Descartes rules of signs it has 2 or zero positive real roots.

Now   [change signs of coefficient with odd degree of x]

Here we have two sign change from first to the second term and from fourth to the constant term.

Therefore by Descartes rules of signs f(x) has 2 or zero negative real roots.

As it is 4th degree polynomial so it can have 4 roots and complex roots occur in pair so f(x) can have 4 or 2 or 0 complex roots.

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step-by-step explanation:

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it