Question

If $x^2$ - x + a - 3 < 0 for at least one negative value of x, then complete set of values of a

• A. (
• B. (
• C. (
• D. (

Answer 1

The correct option is C

(

For real roots, D $\ge$ 0 $\Rightarrow$ a $\le$ $\frac{13}{4}$

Both roots will be non - negative if D $\ge$ 0 , a - 3 > $\ge$ 0 ; $\Rightarrow$ a $\in$ $[3,\frac{13}{4}]$

$\therefore$ for at least one negative root if a $\in$ $(-\infty ,\frac{13}{4})$ ~ $[3,\frac{13}{4}]$

$\Rightarrow$ a $\in$$(-\infty ,3)$