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Find the discriminant.\newline3u2+9u+6=03u^2 + 9u + 6 = 0

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Full solution

Q. Find the discriminant.\newline3u2+9u+6=03u^2 + 9u + 6 = 0
  1. Identify coefficients: Identify the coefficients aa, bb, and cc from the quadratic equation 3u2+9u+6=03u^2 + 9u + 6 = 0 by comparing it to the standard form ax2+bx+c=0ax^2 + bx + c = 0. Here, a=3a = 3, b=9b = 9, and c=6c = 6.
  2. Calculate discriminant: Calculate the discriminant using the formula D=b2−4acD = b^2 - 4ac. Substitute the identified values into the formula: D=(9)2−4×3×6D = (9)^2 - 4 \times 3 \times 6.
  3. Perform calculations: Perform the calculations: D=81−4×3×6D = 81 - 4 \times 3 \times 6. First, calculate 4×3×6=12×6=724 \times 3 \times 6 = 12 \times 6 = 72. Then, subtract this from 8181: D=81−72D = 81 - 72.
  4. Find discriminant: Complete the subtraction to find the discriminant: D=81−72=9D = 81 - 72 = 9.

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