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Find the discriminant.\newline7r2−r+5=07r^2 - r + 5 = 0

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Full solution

Q. Find the discriminant.\newline7r2−r+5=07r^2 - r + 5 = 0
  1. Identify values: Identify the values of aa, bb, and cc from the quadratic equation in the form ax2+bx+c=0ax^2 + bx + c = 0. Comparing 7r2−r+5=07r^2 - r + 5 = 0 with ax2+bx+c=0ax^2 + bx + c = 0, we find: a=7a = 7 b=−1b = -1 c=5c = 5
  2. Calculate discriminant: Use the discriminant formula D=b2−4acD = b^2 - 4ac to calculate the discriminant of the quadratic equation.\newlineSubstitute 77 for aa, −1-1 for bb, and 55 for cc in the formula.\newlineD=(−1)2−4×7×5D = (-1)^2 - 4 \times 7 \times 5
  3. Find value: Perform the calculations to find the value of the discriminant.\newlineD=1−4×7×5D = 1 - 4 \times 7 \times 5\newlineD=1−140D = 1 - 140\newlineD=−139D = -139

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