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Mathematics

If x2 - 3x + 2 = 0, values of x correct to one decimal place are :

  1. 2.0 and 1.0

  2. 2.0 or 1.0

  3. 3.0 and 2.0

  4. 3.0 or 2.0

Quadratic Equations

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Answer

Comparing equation x2 - 3x + 2 = 0 with ax2 + bx + c = 0, we get :

a = 1, b = -3 and c = 2.

By formula,

x = b±b24ac2a\dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Substituting values we get :

x=(3)±(3)24×1×22×1=3±982=3±12=3±12=3+12 or 312=42 or 22=2.0 or 1.0x = \dfrac{-(-3) \pm \sqrt{(-3)^2 - 4 \times 1 \times 2}}{2 \times 1} \\[1em] = \dfrac{3 \pm \sqrt{9 - 8}}{2} \\[1em] = \dfrac{3 \pm \sqrt{1}}{2} \\[1em] = \dfrac{3 \pm 1}{2} \\[1em] = \dfrac{3 + 1}{2} \text{ or } \dfrac{3 - 1}{2} \\[1em] = \dfrac{4}{2} \text{ or } \dfrac{2}{2} \\[1em] = 2.0 \text{ or } 1.0

Hence, Option 2 is the correct option.

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