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Find the discriminant.\newline7x2+9x−2=07x^2 + 9x - 2 = 0

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Full solution

Q. Find the discriminant.\newline7x2+9x−2=07x^2 + 9x - 2 = 0
  1. Identify values: Identify the values of aa, bb, and cc from the quadratic equation in the form ax2+bx+c=0ax^2 + bx + c = 0. Comparing 7x2+9x−2=07x^2 + 9x - 2 = 0 with ax2+bx+c=0ax^2 + bx + c = 0, we find: a=7a = 7 b=9b = 9 c=−2c = -2
  2. Use discriminant formula: Use the discriminant formula D=b2−4acD = b^2 - 4ac to find the discriminant of the quadratic equation.\newlineSubstitute the identified values into the formula:\newlineD=(9)2−4×7×(−2)D = (9)^2 - 4 \times 7 \times (-2)
  3. Calculate discriminant: Calculate the discriminant using the substituted values.\newlineD=81−(−56)D = 81 - (-56)\newlineD=81+56D = 81 + 56\newlineD=137D = 137

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