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Find the discriminant.\newline7x2−4x−4=07x^2 - 4x - 4 = 0

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Full solution

Q. Find the discriminant.\newline7x2−4x−4=07x^2 - 4x - 4 = 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 7x2−4x−4=07x^2 - 4x - 4 = 0 with ax2+bx+c=0ax^2 + bx + c = 0, we find: a=7a = 7 b=−4b = -4 c=−4c = -4
  2. Calculate discriminant: Calculate the discriminant using the formula D=b2−4acD = b^2 - 4ac.\newlineSubstitute 77 for aa, −4-4 for bb, and −4-4 for cc in the formula.\newlineD=(−4)2−4×7×(−4)D = (-4)^2 - 4 \times 7 \times (-4)
  3. Simplify discriminant: Simplify the discriminant.\newlineD=16−(−112)D = 16 - (-112)\newlineD=16+112D = 16 + 112\newlineD=128D = 128

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