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Find the discriminant.\newline9y2+7y+4=09y^2 + 7y + 4 = 0

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Full solution

Q. Find the discriminant.\newline9y2+7y+4=09y^2 + 7y + 4 = 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 9y2+7y+4=09y^2 + 7y + 4 = 0, we have: a=9a = 9 b=7b = 7 c=4c = 4
  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 into formula: Substitute the identified values into the discriminant formula.\newlineD=b2−4acD = b^2 - 4ac\newlineD=(7)2−4×9×4D = (7)^2 - 4 \times 9 \times 4
  4. Calculate discriminant: Calculate the discriminant.\newlineD=49−4×9×4D = 49 - 4 \times 9 \times 4\newlineD=49−144D = 49 - 144\newlineD=−95D = -95

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