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Find the discriminant.\newline5r2−3r+2=05r^2 - 3r + 2 = 0

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Full solution

Q. Find the discriminant.\newline5r2−3r+2=05r^2 - 3r + 2 = 0
  1. Identify values of aa, bb, cc: Identify the values of aa, bb, and cc from the quadratic equation in the form ax2+bx+c=0ax^2 + bx + c = 0. Comparing 5r2−3r+2=05r^2 - 3r + 2 = 0 with ax2+bx+c=0ax^2 + bx + c = 0, we find: a=5a = 5 bb00 bb11
  2. Calculate discriminant: Calculate the discriminant using the formula D=b2−4acD = b^2 - 4ac. Substitute 55 for aa, −3-3 for bb, and 22 for cc in the formula. D=(−3)2−4×5×2D = (-3)^2 - 4 \times 5 \times 2
  3. Simplify discriminant: Simplify the discriminant. \newlineD=9−4×5×2D = 9 - 4 \times 5 \times 2\newlineD=9−40D = 9 - 40\newlineD=−31D = -31

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