Book Online Demo

Check Your IQ

Try Test

Courses

For what value(s) of ‘a’ quadratic equation $30 a x^{2} - 6 x + 1 = 0$ has no real roots?

see full answer

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

a = \frac{3}{10}

a < \frac{3}{10}

a > \frac{1}{10}

a > \frac{3}{10}

answer is D.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Given quadratic equation is

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

.
For no real roots, D<0 where

D = b^{2} - 4 ac

.
Now comparing

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

with

a x^{2} + bx + c = 0

we get,

a = 30 a, b = - 6, c = 1

Substituting the values in D,

\Rightarrow 0 > b^{2} - 4 ac

\Rightarrow 0 > {(- 6)}^{2} - 4 (30 a) (1)

\Rightarrow 0 > 36 - 120 a

\Rightarrow 120 a > 36

\Rightarrow a > \frac{36}{120}

\Rightarrow a > \frac{3}{10}

Thus, for all values of a greater than

\frac{3}{10},

the given quadratic equation will have imaginary roots.
Therefore, option (4) is correct.

Watch 3-min video & get full concept clarity