Question

find the zeros of a(x2+1)-x(a2+1) quadratic polynomial and verify the relationship between the zeros and their coefficients

Answer 1

In the attachment I have found out zeros of the quadratic polynomial
by factorization method.

After that I verified the relation between
the coefficients and zeros.

I hope that this answer help you
.
.
.
Karups

Answer 2

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 .

Hence, it is solved .