Math, asked by smartstudent77, 30 days ago

Using quadratic formula, solve p²x² + (p² - q²)x - q² = 0.​

Answers

Answered by sudharose315
0

Step-by-step explanation:We have p  

2

x  

2

+(p  

2

−q  

2

)x−q  

2

=0

Comparing this equation to ax  

2

+bx+c=0, we have

a=p  

2

,b=p  

2

−q  

2

 and c=−q  

2

 

∴ D−D=b  

2

−4ac=(p  

2

−q  

2

)  

2

−4×p  

2

+(−q)  

2

 

=(p  

2

−q  

2

)  

2

+4p  

2

q  

2

=(p  

2

−q  

2

)  

2

>0

So, the given equation has real roots given by

α=  

2a

−b+  

D

​  

 

​  

=  

2p  

2

 

(p  

2

−q  

2

)+(p  

2

+q  

2

)

​  

=  

2p  

2

 

2q  

2

 

​  

=  

p  

2

 

q  

2

 

​  

 

and β=  

2a

−b−  

D

​  

 

​  

=  

2p  

2

 

−(p  

2

−q  

2

)−(p  

2

+q  

2

)

​  

=  

2p  

2

 

−2q  

2

 

​  

=−1

Hence roots are  

p  

2

 

q  

2

 

​  

 and −1

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