In the following, determine whether the given quadratic equations have real roots and if so, fin...
In the following, determine whether the given quadratic equations have real roots and if so, find the roots:
(i) \( 16 x^{2}=24 x+1 \)
(ii) \( x^{2}+x+2=0 \)
(iii) \( \sqrt{3} x^{2}+10 x-8 \sqrt{3}=0 \)
(iv) \( 3 x^{2}-2 x+2=0 \)
(v) \( 2 x^{2}-2 \sqrt{6} x+3=0 \)
(vi) \( 3 a^{2} x^{2}+8 a b x+4 b^{2}=0, a \neq 0 \)
(vii) \( 3 x^{2}+2 \sqrt{5} x-5=0 \)
(viii) \( x^{2}-2 x+1=0 \)
(ix) \( 2 x^{2}+5 \sqrt{3} x+6=0 \)
(x) \( \sqrt{2} x^{2}+7 x+5 \sqrt{2}=0 \)
(xi) \( 2 x^{2}-2 \sqrt{2} x+1=0 \)
(xii) \( 3 x^{2}-5 x+2=0 \)
\( + \)
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