Question

1. Determine the nature of the roots of the equation.

Answer 1

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3/5 X² - 2/3 X + 1 = 0


3X²/5 - 2X/3 +1 = 0

9X² - 10X + 15 = 0



★ 9X² - 10X + 15


Here,


A = 9 , B = -10 and C = 15



Discriminant (D) = B²-4AC




=> (-10)² - 4 × 9 × 15


=> 100 - 540


=>-440



Here we can see that the discriminant of the given equation is smaller than 0.


So,

the nature of the roots of the given equation has no real roots.




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Answer 2

Compare given Quadratic equation

(3/5)x² - ( 2/3)x + 1 = 0 with

ax² + bx + c = 0 , we get

a = 3/5 ,

b = -2/3 ,

c = 1 ,

Discreminant ( D ) = b² - 4ac

= ( -2/3 )² - 4 × (3/5) × 1

= 4/9 - 12/5

= ( 20 - 108 )/45

= -88/45

D < 0

Therefore ,

Roots are not real .

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