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Find the discriminant.\newline8p2+8p+2=08p^2 + 8p + 2 = 0

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Full solution

Q. Find the discriminant.\newline8p2+8p+2=08p^2 + 8p + 2 = 0
  1. Identify coefficients: Identify the coefficients of the quadratic equation.\newlineThe quadratic equation is in the form ap2+bp+c=0ap^2 + bp + c = 0. For the equation 8p2+8p+2=08p^2 + 8p + 2 = 0, the coefficients are:\newlinea = 88\newlineb = 88\newlinec = 22
  2. Use discriminant formula: Use the discriminant formula.\newlineThe discriminant DD of a quadratic equation ax2+bx+c=0ax^2 + bx + c = 0 is given by D=b2−4acD = b^2 - 4ac. We will substitute the identified coefficients into this formula.
  3. Calculate discriminant: Calculate the discriminant.\newlineSubstitute a=8a = 8, b=8b = 8, and c=2c = 2 into the formula D=b2−4acD = b^2 - 4ac to find the discriminant.\newlineD=(8)2−4×8×2D = (8)^2 - 4 \times 8 \times 2\newlineD=64−64D = 64 - 64\newlineD=0D = 0

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