Home
Class 12
MATHS
If x1, a n dx2 are the roots of x^2+(sin...

If `x_1, a n dx_2` are the roots of `x^2+(sintheta-1)x-1/(2cos^2theta)=0,` then find the maximum value of `x1 2+x2 2dot`

Text Solution

Verified by Experts

The correct Answer is:
4
`x_(1)+x_(2) = ( 1 - sin theta), x_(1)+x_(2) = - (1)/(2) cos^(2) theta`
Now, `x_(1)^(2)+x_(2)^(2) = ( x_(1)+x_(2))^(2) - 2x_(1)+x_(2)`
= ` ( - sin theta)^(2) + cos^(2) theta`
= `2 - 2 sin theta`
`rArr x_(1)^(2)+x_(2)^(2) |_(max)=2 + 2 = 4`
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Exercise 2.10|5 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Exercise 2.11|8 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Exercise 2.8|11 Videos

  • STRAIGHT LINES

    CENGAGE|Exercise JEE Advanced Previous Year|4 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE|Exercise Question Bank|20 Videos

Similar Questions

Explore conceptually related problems

If x_(1), and x_(2) are the roots of x^(2)+(sin theta-1)x-(1)/(2)(cos^(2)theta)=0, then find the maximum value of x_(1)^(2)+x_(2)^(2)

If x_(1) and x_(2) are the roots of x^(2)+(sin theta-1)x-(1)/(2)cos^(2)theta=0 then maximum value of x_(1)^(2)+x_(2)^(2) is equal to

If x + 1/x= 2cos theta ,then find the value of x^3 + 1/x^3

If 2cos theta=x+1/x then 2cos^2 theta=

Let x_(1) and x_(2) be the real roots of the equation x^(2)-(k-2)x+(k^(2)+3k+5)=0 then the maximum value of x_(1)^(2)+x_(2)^(2) is

If x+(1)/(x)=2cos theta, then the value of x^(n)+(1)/(x^(n))

If x + iy = (1)/(1-cos theta + 2 i sin theta), theta ne 2n pi, n in I , then maximum value of x is

If 2 cos theta=x+(1)/(x) , find the value of 2cos 3 theta