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4.2 Quadratic equations and inequations — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS4.2 Quadratic equations and inequations1 Mark
MCQ
The quadratic equation whose one root is $2 - \sqrt 3 $ will be
  • A
    ${x^2} - 4x - 1 = 0$
  • ✓
    ${x^2} - 4x + 1 = 0$
  • C
    ${x^2} + 4x - 1 = 0$
  • D
    ${x^2} + 4x + 1 = 0$
✓

Answer

Correct option: B.
${x^2} - 4x + 1 = 0$
b
(b) Given that first root is $2 - \sqrt 3 $, so other root will be $2 + \sqrt 3 $. Now the sum of roots is $2 - \sqrt 3 + 2 + \sqrt 3 = 4$ and the product of roots $(2 + \sqrt 3 )(2 - \sqrt 3 ) = 4 - 3 = 1$

Hence required equation is ${x^2} - 4x + 1 = 0$.

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