NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 4: Quadatric Equation - Exercise 4.1

Question 6

We are given the quadratic equation: \(2x^2 - kx + k = 0\).

For a quadratic equation \(ax^2 + bx + c = 0\), the condition for equal roots is:

\(D = b^2 - 4ac = 0\), where \(D\) is the discriminant.

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Step 1: Identify \(a\), \(b\), and \(c\) from the equation:

• \(a = 2\) (coefficient of \(x^2\))
• \(b = -k\) (coefficient of \(x\))
• \(c = k\) (constant term)

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Step 2: Write discriminant formula:

\(D = b^2 - 4ac\)

Substitute values:

\(D = (-k)^2 - 4(2)(k)\)

\(D = k^2 - 8k\)

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Step 3: Set discriminant equal to zero (for equal roots):

\(k^2 - 8k = 0\)

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Step 4: Factorize:

\(k(k - 8) = 0\)

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Step 5: Solve each factor:

• If \(k = 0\)
• If \(k - 8 = 0\Rightarrow k = 8\)

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Final Answer: The values of \(k\) are 0 and 8.