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Find the discriminant.\newliner2+6r+9=0r^2 + 6r + 9 = 0

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Full solution

Q. Find the discriminant.\newliner2+6r+9=0r^2 + 6r + 9 = 0
  1. Identify coefficients: Identify the coefficients aa, bb, and cc in the quadratic equation r2+6r+9=0r^2 + 6r + 9 = 0 by comparing it to the standard form ax2+bx+c=0ax^2 + bx + c = 0. For our equation, a=1a = 1, b=6b = 6, and 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 of aa, bb, and cc into the discriminant formula.\newlineSo, D=(6)2−4×1×9D = (6)^2 - 4 \times 1 \times 9.
  4. Calculate discriminant: Calculate the discriminant using the substituted values.\newlineD=36−4×1×9D = 36 - 4 \times 1 \times 9.\newlineD=36−36D = 36 - 36.\newlineD=0D = 0.

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