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Find the discriminant.\newline3t2−6t+1=03t^2 - 6t + 1 = 0

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Full solution

Q. Find the discriminant.\newline3t2−6t+1=03t^2 - 6t + 1 = 0
  1. Identify coefficients: Identify the coefficients aa, bb, and cc from the quadratic equation in the form ax2+bx+c=0ax^2 + bx + c = 0. For the equation 3t2−6t+1=03t^2 - 6t + 1 = 0, we have: a=3a = 3 b=−6b = -6 c=1c = 1
  2. Recall formula for discriminant: Recall the formula for the discriminant of a quadratic equation, which is D=b2−4acD = b^2 - 4ac.
  3. Substitute values into formula: Substitute the identified values of aa, bb, and cc into the discriminant formula.\newlineD=(−6)2−4×3×1D = (-6)^2 - 4 \times 3 \times 1
  4. Calculate discriminant: Calculate the discriminant.\newlineD=36−4×3×1D = 36 - 4 \times 3 \times 1\newlineD=36−12D = 36 - 12\newlineD=24D = 24

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