In this page nature of roots solution1 we are going to see solutions of some practice questions of the worksheet nature of roots.

Determine the nature of the roots of the equation.

(i) x² - 8 x + 12 = 0

To get the values of a , b and c we have to compare the given equation with the general form of quadratic equation a x² + b x + c = 0

a = 1 b = -8 and c = 12

Discriminant ∆ = b² - 4 ac

= (-8)² - 4 (1) (12)

= 64 - 48

= 16

The value of ∆ is 16 that is ∆ > 0 it is a perfect square. Hence the roots are real,unequal and rational.

(ii) 2x² - 3 x + 4 = 0

To get the values of a , b and c we have to compare the given equation with the general form of quadratic equation a x² + b x + c = 0

a = 2 b = -3 and c = 4

Discriminant ∆ = b² - 4 ac

= (-3)² - 4 (2) (4)

= 9 - 32

= - 23

The value of ∆ is -23 that is ∆ < 0 . Hence the roots are imaginary.

(iii) 9 x² + 12 x + 4 = 0

To get the values of a , b and c we have to compare the given equation with the general form of quadratic equation a x² + b x + c = 0

a = 9 b = 12 and c = 4

Discriminant ∆ = b² - 4 ac

= (12)² - 4 (9) (4)

= 144 - 144

= 0

The value of ∆ is 0 . Hence the roots are real and equal.

(iv) 3 x² - 2 √6 x + 2 = 0

a = 3 b = -2 √6 and c = 2

Discriminant ∆ = b² - 4 ac

= (-2√6)² - 4 (3) (2)

= 4 (6) - 244

= 24 - 24

= 0

The value of ∆ is 0 . Hence the roots are real and equal.

nature of roots solution1 nature of roots solution1

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