Find the zeroes of the polynomial a(x²+1) - x(a²+1) and verify the relationship between the zeroes and the coefficients.
Answers
Answer:
Step-by-step explanation:
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 .
therefore x = 1/a or a .
Therefore, Sum of zeros = -( coefficient of x )/( coefficient of x² ) = - B/A
==> 1/a + a = -( -( a² + 1 ) )/ a .
therefore ( 1 + a² )/a = ( 1 + a² )/ a .
And, Product of zeros = Constant term/ coefficient of x² = C/A .
==> 1/a × a = a/a .
therefore, 1 = 1 .
Hope it helps!
Answer:
1/a or a .
Step-by-step explanation :
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 .
hope it helps you ❤️✨