Question

3/5x2 - 2/3x +1 =0 find the nature of roots

Answer 1

Answer:

This equation has no real roots.

Step-by-step explanation:

First we'll check it's discriminant.

D = b^2 - 4ac

Here, a= 3/5, b = -2/3, c=1

So,

(-2/3)^2 - 4(3/5)(1)

= (4/9) - (12/5)

= (20 - 108)/45

= -88/45

As the value of discriminant is less than zero, this equation has no real roots.

Answer 2

Given:

Consider the given equation

$\frac{3}{5}x^2-\frac{2}{3}x+1=0$

Find:

Nature of roots

Solution:

Find discriminant (D) and decide if D <0 then the roots are not real

If D = 0 the roots are real and equal

If D>0 then roots are real and distinct

Here a = 3/5, b = -2/3 c = 1

D = b^2 -4ac

$D=(-2/3)^2-4(3/5)(1)$

$D=-\frac{88}{45} < 0$

therefore the roots are imiaginary that is not real