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Mathematics

If the equation, ax2 + 2x + a = 0 has two real and equal roots, then:

  1. a = 0, 1

  2. a = 1, 1

  3. a = 0, -1

  4. a = -1, 1

Quadratic Equations

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Answer

Comparing ax2 + 2x + a = 0 with ax2 + bx + c = 0 we get,

a = a, b = 2 and c = a.

We know that,

Since equations has real and equal roots,

⇒ D = 0

⇒ b2 - 4ac = 0

⇒ (2)2 - 4(a)(a) = 0

⇒ 4 - 4a2 = 0

⇒ 4 = 4a2

⇒ a2 = 44\dfrac{4}{4}

⇒ a2 = 1

⇒ a = 1\sqrt{1}

⇒ a = ± 1

⇒ a = -1, 1.

Hence, option 4 is the correct option.

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