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sergey [27]
3 years ago
6

Factor 21x^3 y^2 – 3x^2y + 75x^4

Mathematics
1 answer:
malfutka [58]3 years ago
6 0
The greatest common factor is 3x². The rest doesn't factor.
  21x³y² -3x²y +75x⁴ = 3x²(7xy² -y +25x²)
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Please help!
crimeas [40]

Answer:

The zeros are:

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  • The function has three distinct real zeros.

Hence, option (B) is true.

Step-by-step explanation:

Given the expression

h\left(x\right)=\left(x-4\right)^2\left(x^2-7x+\:10\right)

Let us determine the zeros of the function by putting h(x) = 0 and solving the expression

0=\left(x-4\right)^2\left(x^2-7x+10\right)

switch sides

\left(x-4\right)^2\left(x^2-7x+10\right)=0

as

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so

\left(x-4\right)^2\left(x-2\right)\left(x-5\right)=0

Using the zero factor principle

  • \mathrm{If}\:ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)

so

x-4=0\quad \mathrm{or}\quad \:x-2=0\quad \mathrm{or}\quad \:x-5=0

x =4, x=2, x = 5

Thus, the zeros are:

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It is clear that there are three zeros and all the zeros are distinct real numbers.

Therefore,

  • The function has three distinct real zeros.

Hence, option (B) is true.

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