What are the solutions to the equation roots r^3+r^2-23r-35=0 ?

The solutions to the equation roots r^3+r^2-23r-35=0 are r=5,r=-3+sqrt(2),r=-3-sqrt(2)

Find the zeros of roots r^3+r^2-23r-35=0

The zeros of roots r^3+r^2-23r-35=0 are r=5,r=-3+sqrt(2),r=-3-sqrt(2)

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roots

r^{3} + r^{2} - 23 r - 35 = 0

r = 5, r = - 3 + 2, r = - 3 - 2

Solution steps

r^{3} + r^{2} - 23 r - 35 = 0

Factor

r^{3} + r^{2} - 23 r - 35 : (r - 5) (r^{2} + 6 r + 7)

(r - 5) (r^{2} + 6 r + 7) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

r - 5 = 0 or r^{2} + 6 r + 7 = 0

Solve

r - 5 = 0 : r = 5

Solve

r^{2} + 6 r + 7 = 0 : r = - 3 + 2, r = - 3 - 2

The solutions are

r = 5, r = - 3 + 2, r = - 3 - 2

12 x^{4} + 7 x^{3} + 49 x^{2} + 28 x + 4 = 0

0 = 6 x^{2} + x^{3}

x (x + 2) (x + 3) = - 1

3 x^{4} - 16 x^{3} + 24 x^{2} - 9 = 0

y, x^{3} \cdot y = 9

What are the solutions to the equation roots r^3+r^2-23r-35=0 ?
The solutions to the equation roots r^3+r^2-23r-35=0 are r=5,r=-3+sqrt(2),r=-3-sqrt(2)
Find the zeros of roots r^3+r^2-23r-35=0
The zeros of roots r^3+r^2-23r-35=0 are r=5,r=-3+sqrt(2),r=-3-sqrt(2)