Question

For second degree polynomial it is seen that the roots are equal. Then what is the relation between the Rolles point c and the root x?

(a) c = x

(b) c = x^2

(c) They are independent

(d) c = sin(x)

This question was posed to me in an interview.

My question is taken from Rolle’s Theorem in chapter Differential Calculus of Engineering Mathematics

Answer 1

Right option is (a) c = x

Best explanation: For a polynomial with equal roots we can write the polynomial as f(x) = (x – a)^2

Where a is the repeated root.

Differentiating it and equating the function to zero we get the Rolles point,

 f'(x) = 2(x – a) = 0

 x = a = c.