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# Find the Nature of the Roots of the Following Quadratic Equations. If the Real Roots Exist, Find Them 2x^2 - 6x + 3 = 0 - CBSE Class 10 - Mathematics

#### Questions

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

#### Solution

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

Is there an error in this question or solution?

#### APPEARS IN

NCERT Solution for Mathematics Textbook for Class 10 (2019 to Current)