The value(s) of k for which the quadratic equation 2x 2 - kx + k = 0 has equal roots is (are) 1. 0 only 2. 4 3. 8 only 4. 0, 8

Given , 2x 2 - kx + k = 0 has equal roots Comparing equation with ax 2 + bx + c = 0 a= 2 , b = -k , c = k Since, equation has equal roots ∴ b 2 - 4ac = 0 ∴ Option 4 is the correct option.

Mathematics

The value(s) of k for which the quadratic equation 2x² - kx + k = 0 has equal roots is (are)
0 only
4
8 only
0, 8

Quadratic Equations

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Answer

Given ,

2x² - kx + k = 0 has equal roots

Comparing equation with ax² + bx + c = 0
a= 2 , b = -k , c = k

Since, equation has equal roots

∴ b² - 4ac = 0

$\Rightarrow (-k)^2 - 4 \times 2 \times k = 0 \\[0.5em] \Rightarrow k^2 - 8k = 0 \\[0.5em] \Rightarrow k(k - 8) = 0 \\[0.5em] \Rightarrow k = 0 \text{ or } k - 8 = 0 \\[0.5em] k = 0 \text{ or } k = 8 \\[0.5em]$

∴ Option 4 is the correct option.

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Mathematics

The value(s) of k for which the quadratic equation 2x² - kx + k = 0 has equal roots is (are)
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4
8 only
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Quadratic Equations

Answer

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