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Find the discriminant.\newline3y2−y+9=03y^2 - y + 9 = 0

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Full solution

Q. Find the discriminant.\newline3y2−y+9=03y^2 - y + 9 = 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 3y2−y+9=03y^2 - y + 9 = 0, we have: a=3a = 3 b=−1b = -1 c=9c = 9
  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. \newlineD=(−1)2−4×3×9D = (-1)^2 - 4 \times 3 \times 9
  4. Calculate discriminant: Calculate the discriminant.\newlineD=1−4×3×9D = 1 - 4 \times 3 \times 9\newlineD=1−108D = 1 - 108\newlineD=−107D = -107

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