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determine the number of real roots of each polynomial equation. roots of multiplicity
[tex]n[/tex]
are counted
[tex]n[/tex]
times

1.
[tex](x - 4)(x + 3) {}^{2} (x - 1) {}^{3} = 0[/tex]
2.
[tex]x(x + 3)(x - 6) {}^{2} = 0[/tex]
3.
[tex](x {}^{3} - 8)(x {}^{4} + 1) = 0[/tex]


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Sagot :

Kateprecious63idn

Answer:

Determine the number of real roots of each polynomial equation. roots of multiplicity;

1.) ans.

x = 1

x = 1 x = -3

x = 1 x = -3 x = 4

Solve : x-4 = 0

Solve : x-4 = 0 Add 4 to both sides of the equation :

Solve : x-4 = 0 Add 4 to both sides of the equation : x = 4

Solve : (x+3)²= 0

= 0 (x+3) 2 represents, in effect, a product of 2 terms which is equal to zero

= 0 (x+3) 2 represents, in effect, a product of 2 terms which is equal to zero For the product to be zero, at least one of these terms must be zero. Since all these terms are equal to each other, it actually means : x+3 = 0

Subtract 3 from both sides of the equation :

Subtract 3 from both sides of the equation : x = -3

Solve : (x-1)³ = 0

= 0 As explained in step #03.03 above, the equation to be solved is

= 0 As explained in step #03.03 above, the equation to be solved is x-1 = 0

= 0 As explained in step #03.03 above, the equation to be solved is x-1 = 0Add 1 to both sides of the equation :

= 0 As explained in step #03.03 above, the equation to be solved is x-1 = 0Add 1 to both sides of the equation : x = 1

2.) ans.

x = 6

x = 6 x = -3

x = 6 x = -3 x = 0

Solve : x = 0

Solve : x = 0 Solution is x = 0

Solve : x+3 = 0

Solve : x+3 = 0 Subtract 3 from both sides of the equation :

Solve : x+3 = 0 Subtract 3 from both sides of the equation : x = -3

Solve : (x-6)²= 0

Solve : (x-6)² = 0 (x-6)² represents, in effect, a product of 2 terms which is equal to zero

Solve : (x-6)² = 0 (x-6) ²represents, in effect, a product of 2 terms which is equal to zero For the product to be zero, at least one of these terms must be zero. Since all these terms are equal to each other, it actually means : x-6 = 0

3.) ans.

7 solutions were found :

x= 0.7071 - 0.7071 i

x= -0.7071 - 0.7071 i

x= -0.7071 + 0.7071 i

x= 0.7071 + 0.7071 i

x =(-2-√-12)/2=-1-i√ 3 = -1.0000-1.7321i

x =(-2+√-12)/2=-1+i√ 3 = -1.0000+1.7321i

x = 2

sorry tinatamad nako mag sulat ng Solution

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