What are the solutions to the equation roots r^3-7r^2+16r-12 ?

The solutions to the equation roots r^3-7r^2+16r-12 are r=2,r=3

Find the zeros of roots r^3-7r^2+16r-12

The zeros of roots r^3-7r^2+16r-12 are r=2,r=3

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roots

r^{3} - 7 r^{2} + 16 r - 12

r = 2, r = 3

Solution steps

r^{3} - 7 r^{2} + 16 r - 12

The roots are the intercepts with the x-axis

(y = 0)

r^{3} - 7 r^{2} + 16 r - 12 = 0

Factor

r^{3} - 7 r^{2} + 16 r - 12 : (r - 2)^{2} (r - 3)

(r - 2)^{2} (r - 3) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

r - 2 = 0 or r - 3 = 0

Solve

r - 2 = 0 : r = 2

Solve

r - 3 = 0 : r = 3

The solutions are

r = 2, r = 3

x^{3} = 64

6 x^{4} + 5 x^{3} + 25 x^{2} + 20 x + 4 = 0

x^{3} - 2 x^{2} + 62 - 0.5 = 0

x^{4} + 2 x^{2} + 1 = 0

x^{4} - x^{3} + 7 x^{2} - 9 x - 18 = 0

What are the solutions to the equation roots r^3-7r^2+16r-12 ?
The solutions to the equation roots r^3-7r^2+16r-12 are r=2,r=3
Find the zeros of roots r^3-7r^2+16r-12
The zeros of roots r^3-7r^2+16r-12 are r=2,r=3