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Find the discriminant.\newline3x2+6x+3=03x^2 + 6x + 3 = 0

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Full solution

Q. Find the discriminant.\newline3x2+6x+3=03x^2 + 6x + 3 = 0
  1. Identify values: Identify the values of aa, bb, and cc from the quadratic equation ax2+bx+c=0ax^2 + bx + c = 0 by comparing it to 3x2+6x+3=03x^2 + 6x + 3 = 0.\newlineHere, a=3a = 3, b=6b = 6, and c=3c = 3.
  2. Recall formula: Recall the formula for the discriminant of a quadratic equation, which is D=b2−4acD = b^2 - 4ac. We will substitute the identified values of aa, bb, and cc into this formula to find the discriminant.
  3. Substitute values: Substitute 33 for aa, 66 for bb, and 33 for cc in the discriminant formula D=b2−4acD = b^2 - 4ac.\newlineCalculate the discriminant: D=(6)2−4×3×3D = (6)^2 - 4 \times 3 \times 3.
  4. Calculate discriminant: Simplify the discriminant calculation.\newlineD=36−4×3×3D = 36 - 4 \times 3 \times 3\newlineD=36−36D = 36 - 36\newlineD=0D = 0

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