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x^(2)-3x+2=0 How many distinct real solutions does the given equation have?

x2−3x+2=0 x^{2}-3 x+2=0 \newlineHow many distinct real solutions does the given equation have?

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Full solution

Q. x2−3x+2=0 x^{2}-3 x+2=0 \newlineHow many distinct real solutions does the given equation have?
  1. Identify coefficients: Identify the coefficients of aa, bb, and cc in the quadratic equation x2−3x+2=0x^{2} - 3x + 2 = 0. Compare x2−3x+2x^{2} - 3x + 2 with ax2+bx+cax^2 + bx + c to find aa, bb, and cc. a=1a = 1, bb00, bb11
  2. Calculate discriminant: Calculate the discriminant using the formula b2−4acb^2 - 4ac. The discriminant will determine the nature of the roots. Discriminant = (−3)2−4⋅1⋅2(-3)^2 - 4\cdot1\cdot2 Discriminant = 9−89 - 8 Discriminant = 11
  3. Analyze solutions: Analyze the discriminant to determine the number of distinct real solutions. Since the discriminant is positive 1 > 0, there are two distinct real solutions for the equation x2−3x+2=0x^{2} - 3x + 2 = 0.

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