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Determine the solutions of each quadratic equation using the factoring method. x^(2)+5x+6=0 x^(2)-3x-4=0

Determine the solutions of each quadratic equation using the factoring method.\newlinex2−3x−4=0x^{2}-3x-4=0

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Full solution

Q. Determine the solutions of each quadratic equation using the factoring method.\newlinex2−3x−4=0x^{2}-3x-4=0
  1. Factorize Quadratic Equation: Factorize the first quadratic equation x2+5x+6=0x^2 + 5x + 6 = 0. \newline(x+3)(x+2)=0(x + 3)(x + 2) = 0, because 3×2=63 \times 2 = 6 and 3+2=53 + 2 = 5.
  2. Solve for x: Solve for x from the factors of the first equation.\newlinex+3=0→x=−3x + 3 = 0 \rightarrow x = -3\newlinex+2=0→x=−2x + 2 = 0 \rightarrow x = -2
  3. Factorize Second Equation: Factorize the second quadratic equation x2−3x−4=0x^2 - 3x - 4 = 0. \newline(x−4)(x+1)=0(x - 4)(x + 1) = 0, because −4×1=−4-4 \times 1 = -4 and −4+1=−3-4 + 1 = -3.
  4. Solve for x: Solve for x from the factors of the second equation.\newlinex−4=0→x=4x - 4 = 0 \rightarrow x = 4\newlinex+1=0→x=−1x + 1 = 0 \rightarrow x = -1

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