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Find the discriminant.\newline9t2+7t−7=09t^2 + 7t - 7 = 0

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Full solution

Q. Find the discriminant.\newline9t2+7t−7=09t^2 + 7t - 7 = 0
  1. Identify values of aa, bb, cc: Identify the values of aa, bb, and cc from the quadratic equation 9t2+7t−7=09t^2 + 7t - 7 = 0. Comparing at2+bt+c=0at^2 + bt + c = 0 with 9t2+7t−7=09t^2 + 7t - 7 = 0, we find: a=9a = 9 bb00 bb11
  2. Use discriminant formula: Use the discriminant formula D=b2−4acD = b^2 - 4ac to find the discriminant of the quadratic equation.\newlineSubstitute 99 for aa, 77 for bb, and −7-7 for cc in the formula.\newlineD=(7)2−4×9×(−7)D = (7)^2 - 4 \times 9 \times (-7)
  3. Calculate the discriminant: Calculate the discriminant.\newlineD=49−4×9×(−7)D = 49 - 4 \times 9 \times (-7)\newlineD=49+252D = 49 + 252\newlineD=301D = 301

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