Question

Find the value of b if the equation $x^2-x+b=0$ does not possess real roots.

• A. b > $\frac{1}{8}$
• B. b > $\frac{1}{4}$
• C. b > $\frac{1}{2}$
• D. b > 1

Answer 1

The correct option is B

b > $\frac{1}{4}$

Comparing the given equation with the standard form of a quadratic equation, we get

a = 1, b = -1 and c = b
When equation has no real roots, D < 0
$\therefore b^2-4ac<0$
$\Rightarrow (-1{)}^2-4(1\left)\right(b)<0$
$\Rightarrow 1-4b<0$
$\Rightarrow 4b>1$
$\Rightarrow b>\frac{1}{4}$