Question

If abc be non-zero real numbers such that  

                                                                      

Then the equation ax2 + bx + c = 0 will have

Solution

Correct option is

One root between 0 and 1 and other root between 1 and 2

Consider the function Ï• (x) given by  

                               

  

We observe that  

             

              

  

∴ 0, 1 and 2 are the roots of    

By Rolle’s Theorem  will have at least one real root between 0 and 1 and at least one real root between 1 and 2.

SIMILAR QUESTIONS

Q1

Find equation of tangent to the curve 2y = x2 + 3 at (x1y1).

Q2

Find the equation of tangent to the curve y2 = 4ax at (at2, 2at).

Q3

Find the sum of the intercepts on the axes of coordinates by any tangent to the curve,  

                                

Q4

The tangent represented by the graph of the function y = (x) at the point with abscissa x = 1 form an angle π/6 and at the point x = 2 an angle of π/3 and at the point x = 3 an angle π/4. Then find the value of,  

                                                

Q5

Three normals are drawn from the point (c, 0) to the curve y2 = x, show that c must be greater than ½. One normal is always the x-axis. Find c for which the other normals are perpendicular to each other.

Q6

Find the acute angle between the curves y = | x2 – 1| and y = | x2 – 3 | at their points of intersection when x > 0.

Q7

If the relation between subnormal SN and subtangent ST at any point S on the curve; by2 = (x + a)3 is p(SN) = q(ST)2, then find the value of p/q. 

Q8

 in which interval

Q9

If f (x) = xα log x and f (0) = 0, then the value of ‘α’ for which Rolle’s theorem can be applied in [0, 1] is:

Q10

 

Find c of the Lagrange’s mean value theorem for which