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Find the discriminant.\newliner2+2r+1=0r^2 + 2r + 1 = 0

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Full solution

Q. Find the discriminant.\newliner2+2r+1=0r^2 + 2r + 1 = 0
  1. Identify values: Identify the values of aa, bb, and cc by comparing the given equation r2+2r+1=0r^2 + 2r + 1 = 0 with the standard quadratic equation form ax2+bx+c=0ax^2 + bx + c = 0. Here, a=1a = 1, b=2b = 2, and c=1c = 1.
  2. Use discriminant formula: Use the discriminant formula D=b2−4acD = b^2 - 4ac to find the discriminant of the quadratic equation.\newlineSubstitute 11 for aa, 22 for bb, and 11 for cc in the formula.\newlineD=(2)2−4×1×1D = (2)^2 - 4 \times 1 \times 1
  3. Calculate discriminant: Calculate the discriminant.\newlineD=4−4×1×1D = 4 - 4 \times 1 \times 1\newlineD=4−4D = 4 - 4\newlineD=0D = 0

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