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Find the discriminant.\newlinep2+9p+3=0p^2 + 9p + 3 = 0

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Full solution

Q. Find the discriminant.\newlinep2+9p+3=0p^2 + 9p + 3 = 0
  1. Identify values of aa, bb, cc: Identify the values of aa, bb, and cc by comparing the given quadratic equation p2+9p+3=0p^2 + 9p + 3 = 0 with the standard form ax2+bx+c=0ax^2 + bx + c = 0. Here, a=1a = 1, b=9b = 9, and bb00.
  2. Use discriminant formula: Use the discriminant formula D=b2−4acD = b^2 - 4ac to find the discriminant of the quadratic equation.\newlineSubstitute 11 for aa, 99 for bb, and 33 for cc into the formula.\newlineD=(9)2−4×1×3D = (9)^2 - 4 \times 1 \times 3
  3. Calculate discriminant: Calculate the discriminant.\newlineD=81−4×3D = 81 - 4 \times 3\newlineD=81−12D = 81 - 12\newlineD=69D = 69

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