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Find the discriminant.\newline8w2+6w−2=08w^2 + 6w - 2 = 0

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Full solution

Q. Find the discriminant.\newline8w2+6w−2=08w^2 + 6w - 2 = 0
  1. Identify values: Identify the values of aa, bb, and cc from the quadratic equation in the form ax2+bx+c=0ax^2 + bx + c = 0. Comparing 8w2+6w−2=08w^2 + 6w - 2 = 0 with ax2+bx+c=0ax^2 + bx + c = 0, we find: a=8a = 8 b=6b = 6 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 88 for aa, 66 for bb, and −2-2 for cc into the formula.\newlineD=(6)2−4×8×(−2)D = (6)^2 - 4 \times 8 \times (-2)
  3. Find value: Perform the calculations to find the value of the discriminant.\newlineD=36−4×8×(−2)D = 36 - 4 \times 8 \times (-2)\newlineD=36+64D = 36 + 64\newlineD=100D = 100

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