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Mathematics

The roots of the quadratic equation ax2 + x + b = 0 are equal, if :

  1. b2 = 4a

  2. b2 > 4a

  3. b2 > 4b

  4. b = 14a\dfrac{1}{4a}

Quadratic Equations

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Answer

Comparing ax2 + x + b = 0 with the standard form of quadratic equation ax2 + bx + c = 0 we get,

a = a
b = 1
c = b

We know that,

Roots of a quadratic equation are equal if discriminant is equal to zero.

Given,

Roots of the quadratic equation ax2 + x + b = 0 are equal.

∴ b2 - 4ac = 0

⇒ 12 - 4ab = 0 [∵ for the given equation a = a, b = 1 and c = b]

⇒ 1 = 4ab

⇒ b = 14a\dfrac{1}{4a}

Hence, Option 4 is the correct option.

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