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Find the discriminant.\newline2z2−4z+5=02z^2 - 4z + 5 = 0

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Full solution

Q. Find the discriminant.\newline2z2−4z+5=02z^2 - 4z + 5 = 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 2z2−4z+5=02z^2 - 4z + 5 = 0, the coefficients are:\newlinea = 22\newlineb = −4-4\newlinec = 55
  2. Calculate discriminant: Calculate the discriminant using the formula D=b2−4acD = b^2 - 4ac. Substitute the identified values into the formula: D=(−4)2−4×2×5D = (-4)^2 - 4 \times 2 \times 5
  3. Perform calculations: Perform the calculations to find the discriminant.\newlineD=16−4×2×5D = 16 - 4 \times 2 \times 5\newlineD=16−40D = 16 - 40\newlineD=−24D = -24

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