The least positive value of 'a' for which the
equation
2x2 + (a – 10)x + ${{33} \over 2}$
= 2a has real
roots is
Answer (integer)
8
Solution
For real roots Discriminate $\ge$ 0.
<br><br>(a – 10)<sup>2</sup>
– 4$\left( {{{33} \over 2} - 2a} \right).2$ $\ge$ 0
<br><br>$\Rightarrow$ a<sup>2</sup>
+ 100 – 20a – 132 + 16a $\ge$ 0
<br><br>$\Rightarrow$ a
<sup>2</sup>
– 4a – 32 $\ge$ 0
<br><br>$\Rightarrow$ (a – 8) (a + 4) $\ge$ 0
<br><br>$\Rightarrow$ a $\le$ -4 $\cup$ a $\ge$ 8
<br><br>$\therefore$ least positive a = 8
About this question
Subject: Mathematics · Chapter: Complex Numbers and Quadratic Equations · Topic: Complex Numbers and Argand Plane
This question is part of PrepWiser's free JEE Main question bank. 223 more solved questions on Complex Numbers and Quadratic Equations are available — start with the harder ones if your accuracy is >70%.