Question

If a , b , p , q are non zero real numbers , then , how many common roots would two equations 2a²x² - 2ab + b² = 0 , and p²x² + 2pqx + q² = 0 have ?

Answer 1

★ QUADRATIC RESOLUTION ★

For the equation 2a²x² - 2abx + b² = 0

D = 4a²b² - 8a²b² = - 4a² b² < 0

So , obviously , roots are imaginary

Now , for the other equation -

p²x² + 2pqx + q² = 0

D = 4p²q² - 4p² q² = 0

Therefore ,

Roots are real and equal ,

Hence , no common roots possible

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Answer 2

Answer:

Hey here's Your Answer

Step-by-step explanation:

For equation 2a

2

x

2

−abx+b

2

=0

D

1

=4a

2

b

2

−8a

2

b

2

=−4a

2

b

2

<0

Therefore, roots are imaginary.

For equation p

2

x

2

+2pqx+q

2

=0,

D

2

=4p

2

q

2

−4p

2

q

2

=0

Therefore, roots are real and equal.

Hence, no common roots.