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Mathematics

What is the nature of the roots of the equation, 2x2 - 6x + 3 = 0?

  1. rational and unequal

  2. irrational and unequal

  3. real and equal

  4. imaginary and unequal

Quadratic Equations

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Answer

Comparing 2x2 - 6x + 3 = 0 with ax2 + bx + c = 0 we get,

a = 2, b = -6 and c = 3.

We know that,

⇒ D = b2 - 4ac

⇒ D = (-6)2 - 4(2)(3)

⇒ D = 36 - 24

⇒ D = 12

⇒ D > 0 roots are real and unequal.

⇒ D = 12 is not a perfect square, roots are irrational.

Thus, roots are irrational and unequal.

Hence, option 2 is the correct option.

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