Find the Nature of the Roots of the Following Quadratic Equations. If the Real Roots Exist, Find Them 2x^2 - 6x + 3 = 0 - Mathematics

Find the nature of the roots of the following quadratic equations. If the real roots exist, find them

2x² - 6x + 3 = 0

Determine the nature of the roots of the following quadratic equation:

2x² - 6x + 3 = 0

2x² - 6x + 3 = 0

Comparing this equation with ax² + bx + c = 0, we get

a = 2, b = -6, c = 3

Discriminant = b2 - 4ac

= (-6)² - 4 (2) (3)

= 36 - 24 = 12

As b2 - 4ac > 0,

Therefore, distinct real roots exist for this equation

`x = (-b+-b^2-4ac)/(2a)`

`=(-(-6)+-sqrt((-6)^2-4(2)(3)))/(2(2))`

= `(6+-sqrt12)/4=(6+-2sqrt3)/4`

= `(3+-sqrt3)/2`

Therefore the root are `(3+-sqrt3)/2 `

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Chapter 4 Quadratic Equations
Exercise 4.6 | Q 1.2 | Page 41

Chapter 4 Quadratic Equations
Exercise 4.4 | Q 1.3 | Page 91