Question

Find the nature root of the following equation x square - 6x+ 10 =0

Answer 1

Answer:

i)  

x  

2

−3x+5=0

a=2,b=−3,c=5

Discriminant, D=b  

2

−4ac=9−40=−31

Since D<0, the roots are imaginary for the given equation.

ii)  

3x  

2

−4  

3

​

x+4=0

a=3,b=−4  

3

​

,c=4

Discriminant, D=b  

2

−4ac=48−48=0

Since D=0, the roots are real and equal for the given equation.

3x  

2

−4  

3

​

x+4=0

a=3,b=−4  

3

​

,c=4

x=  

2a

[−b±  

b  

2

−4ac

​

]

​

 

x=  

6

4  

3

​

 

​

=  

3

​

 

2

​

 

iii)  

2x  

2

−6x+3=0

a=2,b=−6,c=3

Discriminant, D= b  

2

−4ac=36−24=12

Since D>0, roots are real but not equal.

x=  

2a

[−b±  

b  

2

−4ac

​

]

​

 

x=  

4

6±  

12

​

 

​

 

x=  

4

6±2  

3

​

 

​

 

x=  

2

3±  

3

​

 

​

Step-by-step explanation: