Question

If the roots of the equation 9x^2+4ax+4 = 0 are imaginay then

Answer 1

If the roots of the equation 9x²+4ax+4 = 0 are imaginary then find the range of the a

{complete question}

Given:

The roots of the equation 9x²+4ax+4 = 0 are imaginary

To find:

The range of the a

Solution:

It is given in the question that the roots of the equation 9x²+4ax+4 = 0 are imaginary

So as per the rule of the discriminant, the value of the discriminant must be less than zero.

D < 0

√b²-4ac < 0

We have given the equation as 9x²+4ax+4 = 0

where a = 9, b = 4a and c = 4

√(4a)²-4×9×4 < 0

16a² < 16×9

a² < 9

So the range of the a will be

-3 < a < 3