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For the following quadratic equation, find the discriminant. -6x^(2)-18 x+102=-7x^(2)+2x+2 Answer:

For the following quadratic equation, find the discriminant.\newline−6x2−18x+102=−7x2+2x+2 -6 x^{2}-18 x+102=-7 x^{2}+2 x+2 \newlineAnswer:

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Q. For the following quadratic equation, find the discriminant.\newline−6x2−18x+102=−7x2+2x+2 -6 x^{2}-18 x+102=-7 x^{2}+2 x+2 \newlineAnswer:
  1. Simplify Equation: First, we need to simplify the given quadratic equation by combining like terms on both sides.\newlineThe given equation is:\newline−6x2−18x+102=−7x2+2x+2-6x^{2} - 18x + 102 = -7x^{2} + 2x + 2
  2. Move Terms to One Side: Now, we will move all terms to one side to set the equation to zero.\newlineAdd 7x27x^{2} to both sides:\newline−6x2+7x2−18x+102=2x+2-6x^{2} + 7x^{2} - 18x + 102 = 2x + 2\newlineThis simplifies to:\newlinex2−18x+102=2x+2x^{2} - 18x + 102 = 2x + 2
  3. Standard Form: Next, we subtract 2x2x from both sides and subtract 22 from both sides to get the quadratic equation in standard form:\newlinex2−18x−2x+102−2=0x^{2} - 18x - 2x + 102 - 2 = 0\newlineThis simplifies to:\newlinex2−20x+100=0x^{2} - 20x + 100 = 0
  4. Find Discriminant: Now that we have the quadratic equation in standard form, we can find the discriminant. The discriminant of a quadratic equation ax2+bx+c=0ax^{2} + bx + c = 0 is given by the formula:\newlineDiscriminant (D)=b2−4ac(D) = b^{2} - 4ac
  5. Calculate Discriminant: For our equation x2−20x+100=0x^{2} - 20x + 100 = 0, the coefficients are:\newlinea=1a = 1, b=−20b = -20, and c=100c = 100\newlineLet's plug these values into the discriminant formula:\newlineD=(−20)2−4(1)(100)D = (-20)^{2} - 4(1)(100)
  6. Calculate Discriminant: For our equation x2−20x+100=0x^2 - 20x + 100 = 0, the coefficients are:\newlinea = 11, b = −20-20, and c = 100100\newlineLet's plug these values into the discriminant formula:\newlineD=(−20)2−4(1)(100)D = (-20)^2 - 4(1)(100)Calculate the discriminant:\newlineD=400−400D = 400 - 400\newlineD=0D = 0

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