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(a) Solve the quadratic equation $\sqrt{3}x^2 + 10x + 7\sqrt{3} = 0$ using quadratic formula.
OR
(b) Find the nature of roots of the equation $4x^2 - 4a^2x + a^4 - b^4 = 0, b \neq 0$
OR
(b) Find the nature of roots of the equation $4x^2 - 4a^2x + a^4 - b^4 = 0, b \neq 0$
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(a) Discriminant $= 16$
$x = \frac{-10 \pm \sqrt{16}}{2\sqrt{3}}$
$x = -\frac{3}{\sqrt{3}}, -\frac{7}{\sqrt{3}}$ or $x = -\sqrt{3}, -\frac{7}{3}\sqrt{3}$
OR
(b) Discriminant $= (-4a^2)^2 - 4 \times 4 \times (a^4 - b^4) = 16b^4$
Since, Discriminant $> 0$
Therefore, the given equation has real and distinct roots
$x = \frac{-10 \pm \sqrt{16}}{2\sqrt{3}}$
$x = -\frac{3}{\sqrt{3}}, -\frac{7}{\sqrt{3}}$ or $x = -\sqrt{3}, -\frac{7}{3}\sqrt{3}$
OR
(b) Discriminant $= (-4a^2)^2 - 4 \times 4 \times (a^4 - b^4) = 16b^4$
Since, Discriminant $> 0$
Therefore, the given equation has real and distinct roots