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Determine the number of real solutions for the quadratic equation 2x2−3x+1=02x^2 - 3x + 1 = 0 using the discriminant.

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Full solution

Q. Determine the number of real solutions for the quadratic equation 2x2−3x+1=02x^2 - 3x + 1 = 0 using the discriminant.
  1. Identify values: Identify the values of aa, bb, and cc.\newlineCompare ax2+bx+c=0ax^2 + bx + c = 0 and 2x2−3x+1=02x^2 - 3x + 1 = 0.\newlinea=2a = 2\newlineb=−3b = -3\newlinec=1c = 1
  2. Compare equations: Substitute a=2a = 2, b=−3b = -3, and c=1c = 1 into the discriminant formula D=b2−4acD = b^2 - 4ac.\newlineD=(−3)2−4⋅2⋅1D = (-3)^2 - 4 \cdot 2 \cdot 1
  3. Substitute into formula: Simplify the discriminant.\newlineD=9−8D = 9 - 8
  4. Simplify discriminant: Calculate the final value of the discriminant.\newlineD=1D = 1
  5. Calculate final value: Determine the number of real solutions based on the discriminant.\newlineSince D > 0, there are 22 real solutions.

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