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What is the discriminant of the quadratic equation 7x^(2)-9x-2=0 ? 25 137 -137 -25

What is the discriminant of the quadratic equation 7x2−9x−2=0 7 x^{2}-9 x-2=0 ?\newline2525\newline137137\newline−137 -137 \newline−25 -25

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Q. What is the discriminant of the quadratic equation 7x2−9x−2=0 7 x^{2}-9 x-2=0 ?\newline2525\newline137137\newline−137 -137 \newline−25 -25
  1. Identify Coefficients: The discriminant of a quadratic equation ax2+bx+c=0ax^2 + bx + c = 0 is given by the formula D=b2−4acD = b^2 - 4ac. We need to identify the coefficients aa, bb, and cc from the given quadratic equation and then apply the formula.
  2. Given Quadratic Equation: The given quadratic equation is 7x2−9x−2=07x^2 - 9x - 2 = 0. Here, the coefficient aa is 77, the coefficient bb is −9-9, and the coefficient cc is −2-2.
  3. Calculate Discriminant: Now we will calculate the discriminant using the formula D=b2−4acD = b^2 - 4ac. Substituting the values of aa, bb, and cc, we get D=(−9)2−4(7)(−2)D = (-9)^2 - 4(7)(-2).
  4. Final Result: Calculating the discriminant, we have D=81−4(7)(−2)=81−(−56)=81+56=137D = 81 - 4(7)(-2) = 81 - (-56) = 81 + 56 = 137.

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