Solve 4x ^ 2 – 5x – 12 = 0

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Sanjeev Kumar 2024-04-29T02:44:38+00:00 1 Answer 29 views
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  1. Pawan Kumar
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    2024-04-29T03:16:57+00:00
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    This answer was edited.

    We use a quadratic formula to solve this equation.

    Step 1. Write the Coefficients of the Given equation:

    • The Coefficients of 4x² – 5x – 12 = 0 are:
    • a = 4, b = -5, c = -12

    Step 2. Apply Quadratic Formula:

    • Now, apply the quadratic formula to solve this quadratic equation:
      x = (-b ± √(b² – 4ac)) / 2a

    Step 3. Substitute the value of a, b, and c into the quadratic formula:

    • x = – (-5) ± √(-5)² – 4  (4) -12) / 2 (4)

    Step 4. Simplify the expression inside the square root:

    • x = 5 ± √(25 – (16) (-12) / 8
    • x = 5 ± √(25 + 192) / 8
    • x = (5 ± √217) / 8

    Step 5. Isolate the two possible solutions:

    • x₁ = (5 + √217) / 8
    • x₂ = (5 – √217) / 8

    Key Points:

    • 4x² – 5x – 12 = 0 is an example of the quadratic equation.
    • Every quadratic equation can have at most two real roots.
    • The standard form of quadratic equation is ax² + bx + c = 0, a ≠ 0.
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