Question

Find the nature of the roots of the given quadratic equation, if
real roots exist, find them
2x² – 5x + 3 = 0.​

Answer 1

Answer:

To find nature of the roots, we find the value of the discriminant.

= b² - 4ac = (-5)² - 4(2)(3)

= 25 - 24

= 1

As discriminant > 0, there are real and distinct roots.

We can find the roots by using the quadratic formula.

x = [-b ±√(b²-4ac)]/2a

= [5 ±√1]/2(2)

= ( 5 ± 1)/4

The two zeroes are :

i) = (5 + 1)/4

= 6/4

= 3/2 (or) 1.5

ii) = (5 - 1)/4

= 4/4

= 1

Answer 2

Answer:

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