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Values of k for which the quadratic equation 2x2 – kx + k = 0 has equal roots is ______. - Mathematics

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MCQ
Fill in the Blanks

Values of k for which the quadratic equation 2x2 – kx + k = 0 has equal roots is ______.

Options

  • 0 only

  • 4

  • 8 only

  • 0, 8

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Solution

Values of k for which the quadratic equation 2x2 – kx + k = 0 has equal roots is 0, 8.

Explanation:

Given equation is 2x2 – kx + k = 0

On comparing with ax2 + bx + c = 0, we get

a = 2,b = -k and c = k

For equal roots, the discriminant must be zero

i.e., D = b2 – 4ac = 0

⇒ (–k)2 – 4(2)k = 0

⇒ k2 – 8k = 0

⇒ k(k – 8) = 0

∴ k = 0, 8

Hence, the required values of k are 0 and 8.

Concept: Nature of Roots
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APPEARS IN

NCERT Mathematics Exemplar Class 10
Chapter 4 Quadatric Euation
Exercise 4.1 | Q 6 | Page 37
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