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Find the discriminant.\newline6q2−6q+6=06q^2 - 6q + 6 = 0

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Full solution

Q. Find the discriminant.\newline6q2−6q+6=06q^2 - 6q + 6 = 0
  1. Identify coefficients: Identify the coefficients aa, bb, and cc from the quadratic equation 6q2−6q+6=06q^2 - 6q + 6 = 0 by comparing it to the standard form ax2+bx+c=0ax^2 + bx + c = 0. Here, a=6a = 6, b=−6b = -6, and c=6c = 6.
  2. Recall discriminant 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 into the discriminant formula: D=(−6)2−4⋅6⋅6D = (-6)^2 - 4 \cdot 6 \cdot 6.
  4. Calculate discriminant: Calculate the discriminant: D=36−4×6×6D = 36 - 4 \times 6 \times 6.
  5. Perform multiplication and subtraction: Perform the multiplication and subtraction: D=36−144D = 36 - 144.
  6. Complete calculation: Complete the calculation: D=−108D = -108.

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