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Find the discriminant.\newline2z2−2z+4=02z^2 - 2z + 4 = 0

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Full solution

Q. Find the discriminant.\newline2z2−2z+4=02z^2 - 2z + 4 = 0
  1. Identify coefficients: Identify the coefficients of the quadratic equation.\newlineThe quadratic equation is in the form az2+bz+c=0az^2 + bz + c = 0. For the equation 2z2−2z+4=02z^2 - 2z + 4 = 0, the coefficients are:\newlinea = 22\newlineb = −2-2\newlinec = 44
  2. Calculate discriminant: Calculate the discriminant using the formula D=b2−4acD = b^2 - 4ac.\newlineSubstitute the identified values into the discriminant formula:\newlineD=(−2)2−4×2×4D = (-2)^2 - 4 \times 2 \times 4
  3. Simplify calculation: Simplify the discriminant calculation. \newlineD=4−32D = 4 - 32\newlineD=−28D = -28

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