MCQ
If the equation $x^2- bx + 1 = 0$ does not possess real roots, then :
- A$-3 < b < 3$
- ✓$-2 < b < 2$
- C$b > 2$
- D$b < -2$
✓
Answer
Correct option: B.
$-2 < b < 2$
In the equation
$x^2-b x+1=0$
$\Rightarrow D=b^2-4 a c$
$\Rightarrow D=(-b)^2-4 \times 1 \times 1$
$\Rightarrow D=b^2-4$
$\because$ The roots are not real
$\therefore D < 0$
$\Rightarrow b^2-4<0$
$\Rightarrow b^2<4$
$\text{b}^2<(\pm2)^2$
$\therefore b < 2$ and $b > -2$ or $-2 < b$
$\therefore -2 < b < 2$
$x^2-b x+1=0$
$\Rightarrow D=b^2-4 a c$
$\Rightarrow D=(-b)^2-4 \times 1 \times 1$
$\Rightarrow D=b^2-4$
$\because$ The roots are not real
$\therefore D < 0$
$\Rightarrow b^2-4<0$
$\Rightarrow b^2<4$
$\text{b}^2<(\pm2)^2$
$\therefore b < 2$ and $b > -2$ or $-2 < b$
$\therefore -2 < b < 2$
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