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For the following quadratic equation, find the discriminant. 5x^(2)-78 x+471=-8x-4 Answer:

For the following quadratic equation, find the discriminant.\newline5x2−78x+471=−8x−4 5 x^{2}-78 x+471=-8 x-4 \newlineAnswer:

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Full solution

Q. For the following quadratic equation, find the discriminant.\newline5x2−78x+471=−8x−4 5 x^{2}-78 x+471=-8 x-4 \newlineAnswer:
  1. Bring to Standard Form: First, we need to bring the equation to standard quadratic form ax2+bx+c=0ax^2 + bx + c = 0. We do this by adding 8x8x and 44 to both sides of the equation. 5x2−78x+471+8x+4=05x^2 - 78x + 471 + 8x + 4 = 0
  2. Combine Like Terms: Now, combine like terms to simplify the equation.\newline5x2−(78x−8x)+(471+4)=05x^2 - (78x - 8x) + (471 + 4) = 0\newline5x2−70x+475=05x^2 - 70x + 475 = 0
  3. Identify Quadratic Form: The standard form of a quadratic equation is ax2+bx+c=0ax^2 + bx + c = 0. In this case, a=5a = 5, b=−70b = -70, and c=475c = 475. The discriminant of a quadratic equation is given by the formula D=b2−4acD = b^2 - 4ac.
  4. Substitute into Discriminant Formula: Substitute the values of aa, bb, and cc into the discriminant formula.D=(−70)2−4(5)(475)D = (-70)^2 - 4(5)(475)
  5. Calculate Discriminant: Calculate the discriminant.\newlineD=4900−4(5)(475)D = 4900 - 4(5)(475)\newlineD=4900−9500D = 4900 - 9500
  6. Finalize Calculation: Finish the calculation to find the value of the discriminant. D=−4600D = -4600

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