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algebra · worked example

Solve 2x² - 3x - 2 = 0 — x = 2 or x = -1/2

Method: द्विघात सूत्र. Verified step-by-step solution with our free AI math solver.
Problem

2x2−3x−2=02x^2 - 3x - 2 = 0

Step-by-step solution

  1. a=2a = 2, b=−3b = -3, c=−2c = -2 की पहचान करें।

  2. विविक्तकर की गणना करें: Δ=(−3)2−4(2)(−2)=9+16=25\Delta = (-3)^2 - 4(2)(-2) = 9 + 16 = 25।

  3. द्विघात सूत्र लागू करें: x=3±252⋅2=3±54x = \frac{3 \pm \sqrt{25}}{2 \cdot 2} = \frac{3 \pm 5}{4}।

  4. दो हल: x1=3+54=2x_1 = \frac{3 + 5}{4} = 2 और x2=3−54=−12x_2 = \frac{3 - 5}{4} = -\frac{1}{2}।

Answer

x=2orx=−12x = 2 \quad \text{or} \quad x = -\tfrac{1}{2}

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