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Find the discriminant.\newline5z2−3z−9=05z^2 - 3z - 9 = 0

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Full solution

Q. Find the discriminant.\newline5z2−3z−9=05z^2 - 3z - 9 = 0
  1. Identify coefficients: Identify the coefficients of the quadratic equation.\newlineThe quadratic equation is in the form az2+bz+c=0az^2 + bz + c = 0. For the equation 5z2−3z−9=05z^2 - 3z - 9 = 0, the coefficients are:\newlinea = 55\newlineb = −3-3\newlinec = −9-9
  2. Calculate discriminant: Calculate the discriminant using the formula D=b2−4acD = b^2 - 4ac.\newlineSubstitute the identified values into the formula:\newlineD=(−3)2−4×5×(−9)D = (-3)^2 - 4 \times 5 \times (-9)
  3. Perform calculations: Perform the calculations to find the discriminant.\newlineD=9−(−180)D = 9 - (-180)\newlineD=9+180D = 9 + 180\newlineD=189D = 189

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