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Find the discriminant.\newliner2+9r+5=0r^2 + 9r + 5 = 0

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Full solution

Q. Find the discriminant.\newliner2+9r+5=0r^2 + 9r + 5 = 0
  1. Identify coefficients: Identify the coefficients of the quadratic equation.\newlineThe quadratic equation is in the form ar2+br+c=0ar^2 + br + c = 0. For the equation r2+9r+5=0r^2 + 9r + 5 = 0, the coefficients are:\newlinea = 11 (coefficient of r2r^2)\newlineb = 99 (coefficient of rr)\newlinec = 55 (constant term)
  2. Calculate discriminant: Calculate the discriminant using the formula D=b2−4acD = b^2 - 4ac.\newlineSubstitute the identified values into the discriminant formula:\newlineD=b2−4acD = b^2 - 4ac\newlineD=(9)2−4(1)(5)D = (9)^2 - 4(1)(5)
  3. Perform calculations: Perform the calculations to find the value of the discriminant.\newlineD=81−4(1)(5)D = 81 - 4(1)(5)\newlineD=81−20D = 81 - 20\newlineD=61D = 61

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