Question

( b^{2}-4 a c=0 ) real ( varepsilon ) eanal
( b^{2}-4 a c>0 ) real si un equal ( b^{2}-4 a c<0 ) unequal imaginano
1) ( 2 x^{2}-3 x+5>0 )
( (-3)^{2}-4(2)(5) )
( =9-40 )
( begin{aligned} &=-31<0 text { [Unequal } & text { a imaginary } ] end{aligned} )
ii ( ] 3 x^{2}-4 sqrt{3} x+4 )
( =(-4 sqrt{3})^{2}-4(3)(4)=0 )
( [text { real cunequal }] )
"iil ( 2 x^{2}-6 x+3=0 Rightarrow(-6)^{2}-4(2)(3) )

# ILLUSTRATION : 6 Find the nature of the roots of the following quadratic equations. If the real roots exist, find them: (1) 2x² – 3x +5=0 (ii) 3x2 - 413x +4= 0 (ii) 2x2 - 6x +3=0

Solution