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Choose the correct answer from the given four options : If the equation 2x² – 5x + (k + 3) = 0 has equal roots then the value of k is - Mathematics

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MCQ

Choose the correct answer from the given four options :

If the equation 2x² – 5x + (k + 3) = 0 has equal roots then the value of k is

Options

  • `(9)/(8)`

  • `-(9)/(8)`

  • `(1)/(8)`

  • `-(1)/(8)`

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Solution

2x² – 5x + (k + 3) = 0
a = 2, b = –5, c = k + 3
∴ b2 – 4ac
= (–5)2 – 4 x 2 x (k + 3)
= 25 – 8(k + 3)
∴ Roots are equal.
∴ b2 – 4ac = 0
∴ 25 – 8(k + 3) = 0
25 – 8k - 24 = 0
1 – 8k = 0
⇒ 8k = 1

∴ k = `(1)/(8)`.

Concept: Nature of Roots
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