Which of the following equations has real roots ?  Choose the correct choice.
A) 3x2 + 4x + 5 = 0  B) x2 + x + 4 = 0  C) (x - 1)(2x - 5) = 0  D) 2x2 - 3x + 4 = 0  E) None of these
Sol.(c) Roots of a quadratic equation   ax2 + bx + c = 0 are real if b2 - 4ac ≥ 0   Let us work with options as follows.   Option (a) : 3x2 + 4x + 5 = 0   b2 - 4ac = 42 - 4(3)(5) = -44 &lt; 0.   Thus, roots are not real.   (b) : x2 + x + 4 = 0   b2 - 4ac = 12 - 4(1)(4) = 1 - 16 = -15 &lt; 0. Thus, roots are not real. (c) :(x –1) (2x – 5) = 0 =&gt; 22 - 7x + 5 = 0   b2 - 4ac = (-7)2 - 4(2)(5) = 49 - 40= 
<gadget id="calculator">49 - 40</gadget>
<output>9</output>
9 &gt; 0.   Thus roots are real.   or x= 1 and x = 5/2 &gt; 0; Thus, equation has real roots.   (d) : 2x2 - 3x + 4 = 0   b2 - 4ac = (-3)2 - 4(2)(4) = 9 - 32 = -23 &lt; 0.   Thus, roots are not real. Hence, option (c) is correct.   Answer (x - 1)(2x - 5) = 0
<result>C</result>
Which of the following equations has real roots ?