Question

For what value(s) of 'a' quadratic equation 30 ax2 - 6x + 1 = 0 has no real roots?​

Answer 1

Step-by-step explanation:

The given quadratic equation is

$30a {x}^{2} - 6x + 1 = 0$

To have no real roots, its discriminant should be less than 0

So,

$( - 6)^{2} - 4 \times 30a \times 1 < 0$

$\implies36 - 120a < 0$

$\implies120a - 30 > 0$

$\implies \: a > \frac{30}{120}$

$\implies \: a > \frac{1}{4}$