Question

2n square + 5n - 1= 0 discuss the nature of the root​

Answer 1

Answer:

roots are distinct and rational

Answer 2

Given to find the nature of roots of Quadratic equation:-

• 2n² + 5n - 1 = 0

SOLUTION:-

Nature of the Quadratic equation is determined by Discriminant of Quadratic equation Discriminant is denoted by D Discriminant of Quadratic equation is b² - 4ac There are various cases for the nature of roots

❒ D= 0 Roots are real and equal

❒ D<0 Roots are complex and conjugate to each other

❒D>0 Roots are real and distinct

Now , We shall find Discriminant of Quadratic equation

2n² + 5n - 1 = 0 comparing with ax² + bx + c

• a = 2
• b = 5
• c = -1

D = b²- 4ac

D = (5)² -4(2)(-1)

D = 25 + 8

D = 33

Discriminant is 33

Hence ,

33>0 Since D>0 So, roots are real and distinct

So, the nature of above Quadratic equation is real and distinct

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#Know more :-

• Quadratic equation is the equation which is having degree 2
• Quadratic equation has 2 roots
• We can find the 2 roots by different methods like factorisation method, Quadratic formula, complete squaring method
• The general form of Quadratic equation is ax² + bx + c =0