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  4. The roots of the quadratic equation x2-2√3x-22 = 0 are :

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Q. The roots of the quadratic equation $x^{2}-2\sqrt{3}x-22 = 0 $ are :

WBJEEWBJEE 2010Complex Numbers and Quadratic Equations

Solution:

Given, $x^{2}-2 \sqrt{3} x-22=0$
$D=b^{2}-4 a c=12+4 \times 22=100>0$
$\therefore $ Roots are irrational, real and unequal.