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solve the quadratic equation z^(2)+4z-5=0

Solve the quadratic equation z2+4z−5=0 z^{2}+4 z-5=0

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Full solution

Q. Solve the quadratic equation z2+4z−5=0 z^{2}+4 z-5=0
  1. Identify Coefficients: Step Title: Identify the Coefficients\newlineConcise Step Description: Identify the coefficients of the quadratic equation, which are the numbers in front of the variables. In this case, the coefficients are 11, 44, and −5-5.\newlineStep Calculation: Coefficients are 11, 44, −5-5\newlineStep Output: Coefficients: 11, 44, −5-5
  2. Find Factors: Step Title: Find the Factors\newlineConcise Step Description: Find two numbers that multiply to −5-5 (the last term) and add to 44 (the coefficient of the middle term).\newlineStep Calculation: Factors of −5-5 that add up to 44 are 55 and −1-1.\newlineStep Output: Factors: 55, −1-1
  3. Write Factored Form: Step Title: Write the Factored Form\newlineConcise Step Description: Write the factored form of the quadratic equation using the factors found in the previous step.\newlineStep Calculation: The factored form is (z+5)(z−1)(z + 5)(z - 1).\newlineStep Output: Factored Form: (z+5)(z−1)(z + 5)(z - 1)

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