NEW
New Website Launch
Experience the best way to solve previous year questions with mock tests (very detailed analysis), bookmark your favourite questions, practice etc...
1

### WB JEE 2009

Subjective

Find the values of a for which the expression $${x^2} - (3a - 1)x + 2{a^2} + 2a - 11$$ is always positive.

.

## Explanation

Since $${x^2} - (3a - 1)x + 2{a^2} + 2a - 11>0$$ for all x $$\in$$ R

So coefficient of x2 should be greater than 0 and $${b^2} - 4ac < 0$$ i.e., 1 > 0 (coefficient of x2)

and $${(3a - 1)^2} - 4(2{a^2} + 2a - 11) < 0$$

$$\Rightarrow 9{a^2} - 6a + 1 - 8{a^2} - 8a + 44 < 0$$

$$\Rightarrow {a^2} - 14a + 45 < 0$$

$$(a - 5)(a - 9) < 0 \Rightarrow 5 < a < 9$$

### Joint Entrance Examination

JEE Main JEE Advanced WB JEE

### Graduate Aptitude Test in Engineering

GATE CSE GATE ECE GATE EE GATE ME GATE CE GATE PI GATE IN

NEET

Class 12