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Find the discriminant.\newlineu2+4u−4=0u^2 + 4u - 4 = 0

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Full solution

Q. Find the discriminant.\newlineu2+4u−4=0u^2 + 4u - 4 = 0
  1. Identify values: Identify the values of aa, bb, and cc by comparing the given equation u2+4u−4=0u^2 + 4u - 4 = 0 with the standard quadratic equation form ax2+bx+c=0ax^2 + bx + c = 0. Here, a=1a = 1, b=4b = 4, and c=−4c = -4.
  2. Calculate discriminant: Use the discriminant formula D=b2−4acD = b^2 - 4ac to calculate the discriminant of the quadratic equation.\newlineSubstitute 11 for aa, 44 for bb, and −4-4 for cc into the formula.\newlineD=(4)2−4×1×(−4)D = (4)^2 - 4 \times 1 \times (-4)
  3. Perform calculations: Perform the calculations to find the value of the discriminant.\newlineD=16−4×1×(−4)D = 16 - 4 \times 1 \times (-4)\newlineD=16+16D = 16 + 16\newlineD=32D = 32

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