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Find the discriminant.\newline6x2+6x−2=06x^2 + 6x - 2 = 0

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Full solution

Q. Find the discriminant.\newline6x2+6x−2=06x^2 + 6x - 2 = 0
  1. Identify values: Identify the values of aa, bb, and cc from the quadratic equation ax2+bx+c=0ax^2 + bx + c = 0 by comparing it to 6x2+6x−2=06x^2 + 6x - 2 = 0.\newlineHere, a=6a = 6, b=6b = 6, and c=−2c = -2.
  2. Calculate discriminant: Use the discriminant formula D=b2−4acD = b^2 - 4ac to calculate the discriminant of the quadratic equation.\newlineSubstitute 66 for aa, 66 for bb, and −2-2 for cc into the formula.\newlineD=(6)2−4×6×(−2)D = (6)^2 - 4 \times 6 \times (-2)
  3. Find value of discriminant: Perform the calculations to find the value of the discriminant.\newlineD=36−4×6×(−2)D = 36 - 4 \times 6 \times (-2)\newlineD=36+48D = 36 + 48\newlineD=84D = 84

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