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  4. For a given value of k, the product of the roots of x2 - 2kx + 3k2 - 4 = 0 is 5. The roots may be characterised as

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Q. For a given value of $k$, the product of the roots of $x^2 - 2kx + 3k^2 - 4 = 0$ is $5$. The roots may be characterised as

Complex Numbers and Quadratic Equations

Solution:

Since product of the roots $= 5$.
$\therefore 3 \,k^2 - 4 = 5$
$\Rightarrow 3\, k^2 = 9$
$\Rightarrow \, k^2 = 3$.
Now Disc. $= 4k^2 - 4(3k^2 - 4) = 16 - 8\, k^2$
$= 16 - 24 = - 8 < 0 $
$\therefore $ roots are imaginary.