The fundamental theorem of algebra states that a polynomial with degree n has at most n solutions. The "at most" depends on the fact that the solutions might not all be real number.

In fact, if you use complex number, then a polynomial with degree n has exactly n roots.

So, in particular, a third-degree polynomial can have at most 3 roots.

In fact, in general, if the polynomial $p(x)$ has solutions $x_1,\ x_2,\ldots x_n$ , then you can factor it as

$p(x) = (x-x_1)(x-x_2)\ldots (x-x_n)$

So, a third-degree polynomial can't have 4 (or more) solutions, because otherwise you could write it as

$p(x)=(x-x_1)(x-x_2)(x-x_3)(x-x_4)$

But this is a fourth-degree polynomial.

7 0

3 years ago

Please help ASAP!!!!Determine the total number of outcomes.

Cerrena [4.2K]

Answer:

I believe it would be A

Step-by-step explanation:

A deck of cards has 52 cards in it, so it cant be C or D, and with all the possibilities it could not be B

8 0

2 years ago

Multiply 2/3 by 42, and then multiply that product by 10

Mrac [35]

Answer:

140 is the answer

Step-by-step explanation:

2/3 of 42 is 14 multiplied by ten is 140

Hope this helps ;)

7 0

3 years ago

A parallelogram has a length of 15cm and a height of 7.5cm . Calculate it’s area (step by step)

poizon [28]

Answer:

Area of parallelogram is equal to $112.5cm^2$

Step-by-step explanation:

It is given length pf parallelogram which is equal to base of parallelogram is b=15 cm

Height of parallelogram h = 7.5 cm

We have to find the area of the parallelogram.

Area of parallelogram is equal to multiplication of base and height.

Therefore area of parallelogram is,

$A=bh$ , here b is base and h is height.

So $A=15\times 7.5=112.5cm^2$

Therefore area of parallelogram is equal to $112.5cm^2$

3 0

3 years ago