Question

Without solving, comment upon the nature of the roots of the following :
$x { }^{2} - ax - b {}^{2} = 0$
​

Answer 1

Step-by-step explanation:

x^2- ax - b^2 = 0

A= 1,B= -a and C= -b

.. Discriminant B^2=- 4AC

= (-a)^2 -4(1)(-b^2)

= a^2+4b^2 = a positive value.

Since a^2+ 4b^2 is not the perfect square, a

root is irrational.

Since D>0, then the equation has two

irrational and unequal roots.