Home
Class 12
MATHS
If both the roots of x^2-a x+a=0 are gre...

If both the roots of `x^2-a x+a=0` are greater than 2, then find the value of `adot`

Text Solution

Verified by Experts

Both the roots of `x^(2)- ax + a =0 ` are greater than 2 . compare this
equation with `Ax^(2) + Bx + C = 0`. Then , the required conditions are
(i) `D= a^(2) - 4a ge 0 rArr a in (- infty, 0 ]cap(0, infty)`
(ii) `Af (2) gt 0 rArr 1*(4 - 2a + a ) gt 0 rArr a in (-infty ,4)`
`(iii) `- (B)/(2A) gt 1 rArr - (a)/(a) gt 2 rArr a gt 4`
Hence, no such a can be obtained .
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Exercise (Single)|89 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Exercise (Multiple)|38 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Exercise 2.12|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 both the roots of x^(2)-ax+a=0 are greater than 2, then find the value of a .

If both roots of x^(2)-(k-3)x+k=0 are greater than 2, then the range of k is

If both the roots of ax^(2)+ax+1=0 are less than 1, then find the exhaustive range of values of a.

If both the roots of equation x^(2)-mx+9=0 are greater than 2, then m lles in the interval

If both the roots of x^(2)+ax+2=0 lies in the interval (0,3), then find the exhaustive range of value of a.

If x=-2 is one of the roots of the quadratic equation x^(2)+x-2k=0, then find the value of k.

If one root of (k-5)x^(2)-2kx+(k-4)=0 is less than 1 and the other root is greater than 2 then k in (a,b) then the value of a^(2)-b is.

Out of the two roots of x^(2)-2 lambda x+lambda^(2)-1=0 one is greater than 4 and the other root is less than 4, then the limits of lambda are