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Find the discriminant.\newlinez2+4z+4=0z^2 + 4z + 4 = 0

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Full solution

Q. Find the discriminant.\newlinez2+4z+4=0z^2 + 4z + 4 = 0
  1. Identify values: Identify the values of aa, bb, and cc by comparing the given equation z2+4z+4=0z^2 + 4z + 4 = 0 with the standard form of a quadratic equation ax2+bx+c=0ax^2 + bx + c = 0. Here, a=1a = 1, b=4b = 4, and c=4c = 4.
  2. Recall formula: Recall the formula for the discriminant of a quadratic equation, which is D=b2−4acD = b^2 - 4ac.
  3. Substitute values: Substitute the identified values of aa, bb, and cc into the discriminant formula.\newlineSo, D=(4)2−4×1×4D = (4)^2 - 4 \times 1 \times 4.
  4. Perform calculations: Perform the calculations to find the value of the discriminant.\newlineD=16−4×1×4D = 16 - 4 \times 1 \times 4\newlineD=16−16D = 16 - 16\newlineD=0D = 0

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