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=3x^(2)-8x+2=0

=3x2−8x+2=0 =3 x^{2}-8 x+2=0

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Composition of linear and quadratic functions: find a valueright chevron icon

Full solution

Q. =3x2−8x+2=0 =3 x^{2}-8 x+2=0
  1. Identify coefficients: Identify the coefficients of the quadratic equation.\newlineGiven equation: 3x2−8x+2=03x^2 - 8x + 2 = 0\newlineHere, a=3a = 3, b=−8b = -8, c=2c = 2
  2. Apply quadratic formula: Apply the quadratic formula: x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.\newlineCalculation: \newlineb2=(−8)2=64b^2 = (-8)^2 = 64\newline4ac=4×3×2=244ac = 4 \times 3 \times 2 = 24\newlineDiscriminant b2−4acb^2 - 4ac = 6464 - 2424 = 4040
  3. Calculate roots using discriminant: Calculate the roots using the discriminant.\newlinex=−(−8)±402⋅3x = \frac{-(-8) \pm \sqrt{40}}{2 \cdot 3}\newlinex=8±406x = \frac{8 \pm \sqrt{40}}{6}\newline40=2⋅10≈6.32\sqrt{40} = 2 \cdot \sqrt{10} \approx 6.32\newlinex=8±6.326x = \frac{8 \pm 6.32}{6}
  4. Solve for root values: Solve for the specific root values.\newlinex1=8+6.326≈2.387x_1 = \frac{8 + 6.32}{6} \approx 2.387\newlinex2=8−6.326≈0.280x_2 = \frac{8 - 6.32}{6} \approx 0.280

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