2n square + 5n - 1= 0 discuss the nature of the root
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Answer:
roots are distinct and rational
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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
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