Question

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

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

Answer 1

The correct option is B p > $\frac{1}{4}$

On comparing the given equation $x^2-x+p=0$ with standard form $a{x}^2+bx+c=0$, we get

a = 1, b = -1 and c = p

We know that when a quadratic equation has no real roots, discriminant, D < 0.

$\Rightarrow b^2-4ac<0$

$\Rightarrow (-1{)}^2-4(1\left)\right(p)<0$

$\Rightarrow 1-4p<0$

$\Rightarrow 4p>1$

$\Rightarrow p>\frac{1}{4}$