find the factors of a(x²+1)-x(a²+1)
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Answer:
ax² +a -xa²+x
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Answered by
2
Answer:
Answer :-
→ 1/a or a .
We have,
→ A quadratic polynomial :
→ a( x² + 1 ) - x( a² + 1 ) = 0 .
==> ax² + a - x( a² + 1 ) = 0 .
==> ax² - ( a² + 1 )x + a = 0 .
Here, A = a , B = -( a² + 1 ) and C = a .
==> ax² - a²x - x + a = 0 .
==> ax( x - a ) - 1( x - a ) = 0 .
==> ( ax - 1 ) ( x - a ) = 0 .
==> ax - 1 = 0 or x - a = 0 .
•°• x = 1/a or a .
VERIFICATION :)
Therefore, Sum of zeros = -( coefficient of x )/( coefficient of x² ) = - B/A
==> 1/a + a = -( -( a² + 1 ) )/ a .
•°• ( 1 + a² )/a = ( 1 + a² )/ a .
And, Product of zeros = Constant term/ coefficient of x² = C/A .
==> 1/a × a = a/a .
•°• 1 = 1 .
Hence, it is solved .
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