Can you help me to solve 5x^2 + 12x + 19 = 0

Asked by tusharparik11 days ago

Can you help me to solve 5x^2 + 12x + 19 = 0

Answers

admin
11 days ago
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Mathematics - Solving Quadratic Equation 5x² + 12x + 19 = 0

To solve the quadratic equation 5x² + 12x + 19 = 0, we can use the quadratic formula.

Quadratic Formula

x = [-b ± √(b² - 4ac)] / 2a

Solution Steps

  1. Identify the coefficients: a = 5, b = 12, c = 19
  2. Calculate the discriminant (Δ): Δ = b² - 4ac = (12)² - 4 * 5 * 19 = 144 - 380 = -236
  3. Since the discriminant is negative, the equation has complex roots.
  4. Apply the quadratic formula: x = [-12 ± √(-236)] / (2 * 5)
  5. Simplify: x = [-12 ± √(236 * -1)] / 10
  6. x = [-12 ± √(4 * 59 * -1)] / 10
  7. x = [-12 ± 2i√59] / 10
  8. Simplify further: x = (-6 ± i√59) / 5

Complex Solutions

The solutions are x = (-6 + i√59) / 5 and x = (-6 - i√59) / 5, where 'i' is the imaginary unit (√-1).

Note: Complex solutions occur when the discriminant (b² - 4ac) is less than zero. This indicates that the parabola does not intersect the x-axis.

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