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Solve 2x^(3)-24x^(2)+54 x=0 The roots are x= ◻ x= ◻ , and x= ◻

Solve 2x3−24x2+54x=0 2 x^{3}-24 x^{2}+54 x=0 \newlineThe roots are x= x= □ \square x= x= □ \square , and x= x= □ \square

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Q. Solve 2x3−24x2+54x=0 2 x^{3}-24 x^{2}+54 x=0 \newlineThe roots are x= x= □ \square x= x= □ \square , and x= x= □ \square
  1. Factor out GCF: Step 11: Factor out the greatest common factor (GCF) from the equation.\newline2x3−24x2+54x=02x^3 - 24x^2 + 54x = 0\newline=2x(x2−12x+27)=0= 2x(x^2 - 12x + 27) = 0
  2. Set to zero: Step 22: Set each factor to zero and solve for xx.2x=0→x=02x = 0 \rightarrow x = 0x2−12x+27=0x^2 - 12x + 27 = 0
  3. Use quadratic formula: Step 33: Use the quadratic formula to solve x2−12x+27=0x^2 - 12x + 27 = 0.\newlinex=−(−12)±(−12)2−4⋅1⋅272⋅1x = \frac{-(-12) \pm \sqrt{(-12)^2 - 4\cdot1\cdot27}}{2\cdot1}\newlinex=12±144−1082x = \frac{12 \pm \sqrt{144 - 108}}{2}\newlinex=12±362x = \frac{12 \pm \sqrt{36}}{2}\newlinex=12±62x = \frac{12 \pm 6}{2}\newlinex=9,3x = 9, 3

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