Question

1) x2 – ax – b2 = 0
without solving tell the nature of the root
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Answer 1

Step-by-step explanation:

Given   x2 – ax – b2 = 0

without solving tell the nature of the root

• So we have the quadratic equation ax^2 + bx + c and the roots of this equation is
•                      x = - b + - √b^2 – 4ac / 2a  
•        Now the quantity b^2 – 4ac is the discriminant of the polynomial.
• So here we have from the given equation
•  a = 1, b = - a and c = - b^2
•                   So b^2 – 4ac
•                        (- a)^2 – 4(1)(-b^2)
•                     = a^2 + 4b^2  
•  Since this is positive a^2 + 4b^2 = 0 or > 0
•    So it implies a^2 + 4b^2 >=0
• Therefore the given equation can have 2 equal real roots.
• But the roots may be rational or irrational , it depends on the value of coefficients.

Reference link will be

https://brainly.in/question/2818930