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Mathematics

If the roots of the quadratic equation 2x2 + 8x + k = 0 are equal, then the value of k is:

  1. 2

  2. 8

  3. 4

  4. none of these

Quadratic Equations

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Answer

Comparing 2x2 + 8x + k = 0 with ax2 + bx + c = 0 we get,

a = 2, b = 8 and c = k.

We know that,

Since equations has equal roots,

⇒ Discriminant = 0

⇒ b2 - 4ac = 0

⇒ (8)2 - 4(2)(k) = 0

⇒ 64 - 8k = 0

⇒ 8k = 64

⇒ k = 648\dfrac{64}{8}

⇒ k = 8.

Hence, option 2 is the correct option.

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