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For the following quadratic equation, find the discriminant. 12x^(2)-16 x-16=8x^(2) Answer:

For the following quadratic equation, find the discriminant.\newline12x2−16x−16=8x2 12 x^{2}-16 x-16=8 x^{2} \newlineAnswer:

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Full solution

Q. For the following quadratic equation, find the discriminant.\newline12x2−16x−16=8x2 12 x^{2}-16 x-16=8 x^{2} \newlineAnswer:
  1. Bring to Standard Form: First, we need to bring the quadratic equation to standard form, which is ax2+bx+c=0ax^2 + bx + c = 0. We do this by subtracting 8x28x^2 from both sides of the equation.\newlineCalculation: 12x2−16x−16−8x2=012x^2 - 16x - 16 - 8x^2 = 0\newlineSimplified: 4x2−16x−16=04x^2 - 16x - 16 = 0
  2. Identify Coefficients: Next, we identify the coefficients aa, bb, and cc from the standard form of the quadratic equation.\newlineIn our equation, 4x2−16x−16=04x^2 - 16x - 16 = 0, we have:\newlinea=4a = 4, b=−16b = -16, and c=−16c = -16.
  3. Calculate Discriminant: Now, we calculate the discriminant using the formula D=b2−4acD = b^2 - 4ac. Substitute the identified coefficients into the formula. Calculation: D=(−16)2−4(4)(−16)D = (-16)^2 - 4(4)(-16)
  4. Find Value of Discriminant: Perform the calculations to find the value of the discriminant.\newlineCalculation: D=256−4(4)(−16)D = 256 - 4(4)(-16)\newlineCalculation: D=256−(−256)D = 256 - (-256)\newlineCalculation: D=256+256D = 256 + 256\newlineCalculation: D=512D = 512

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