Theory of Equations 5 Question 12

12. The smallest value of k, for which both the roots of the equation x28kx+16(k2k+1)=0 are real, distinct and have values atleast 4 , is

(2009)

Then, the quadratic equation ax2+bx+c=0 has

(a) no root in (0,2)

(b) atleast one root in (1,2)

(c) a double root in (0,2)

(d) two imaginary roots

Objective Questions II

(One or more than one correct option)

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Answer:

Correct Answer: 12. (a)

Solution:

  1. 01/2f(x)dx<0tf(x)dx<03/4f(x)dx

Now, f(x)dx=(1+2x+3x2+4x3)dx

=x+x2+x3+x4

01/2f(x)dx=1516>34,03/4f(x)dx=530256<3



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