Question

If the equation $5x^2–4x+p=0$ has no real roots, then values of $p$ cannot be equal to

• A. $\frac{1}{2}$
  
• B. $\frac{5}{6}$
  
• C. $1$
• D. $\frac{6}{5}$
  

Answer 1

The correct option is A $\frac{1}{2}$


The given quadratic equation $5x^2-4x+p=0$ has no real roots.
$\therefore D<0$
$\Rightarrow (-4{)}^2-4\times 5\times p<0$
$\Rightarrow 16-20p<0$
$\Rightarrow 16<20p$
$\Rightarrow p>\frac{16}{20}$
$\Rightarrow p>\frac{4}{5}$
$\Rightarrow p>0.8$
Thus, $p$ cannot be $\frac{1}{2}$
Hence, the correct answer is option (1).