Without solving , examine the nature of roots of the following quadratic equations:
(i) $25 x^{2} - 10 x + 1 = 0$
(ii) $2 x^{2} + 8 x + 9 = 0$

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Solution

$i) 25 x^{2} - 10 x + 1 = 0$

$b^{2} - 4 a c = 10^{2} - 4 \cdot 25 \cdot 1$

$= 100 - 100$

$b^{2} - 4 a c$ $= 0$ , Equal real roots

$i i) 2 x^{2} + 8 x + 9 = 0$

$b^{2} - 4 a c = 8^{2} - 4 \cdot 2 \cdot 9$

$= 64 - 72$

$b^{2} - 4 a c$ $= - 8$ , imaginary roots.

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Find the nature of the roots of the following quadratic equations:
(i) $2 x^{2} - 8 x + 5 = 0$

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4 $x^{2}$ – 4x + 1 = 0 [2 MARKS]

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