Home
Class 12
MATHS
All possible values of a, so that 6 lies...

All possible values of a, so that 6 lies between the roots of the equation `x^2 + 2(a-3)x +9 =0`

Text Solution

Verified by Experts

Let `f(x)=x^(2)+2(p-3)x+9`, as 6 lies between the roots of `f(x)=0`, we can take `Dgt0` and `afd(6)lt0`
(i) Consider `Dgt0`

`{2(p-3)}^(2)-4.1.9gt0`
`implies(p-3)^(2)-9gt0`
`impliesp(p-6)gt0`
`impliesp epsilon(-oo,0)uu(6,oo)`............i
(ii) Consider `afd(6)lt0`
`1.{36+12(p-3)+9}lt0`
`implies12p+9lt0impliesp+3/4lt0`
`rarrp epsilon(-oo,-3/4)`...........ii
Hence the values of `p` satisfying Eqs (i) and (ii) at the same time are `p epsilon(-oo,-3/4)`.
Promotional Banner

Similar Questions

Explore conceptually related problems

The roots of the equation x^(2)-2sqrt(3)x+3=0 are

The number of real roots of the equation |x|^(2) -3|x| + 2 = 0 , is

Find the roots of the quadratic equation 6x^(2)-x-2=0 .

Find the roots of the equation (1)/(x)-(1)/(x-2)=3, x ne 0,2

The range of values of a so that all the roots of the equations 2x^(3)-3x^(2)-12x+a=0 are real and distinct, belongs to

All the values of m for whilch both the roots of the equation x^2-2m x+m^2-1=0 are greater than -2 but less than 4 lie in the interval

Find the roots of the equation 2x^(2)-5x+3=0 , by factorisation.

Find the roots of the equation 2x^(2)-5x+3=0 , by factorisation.

Find the roots of the quadractic equation 3x^(2) -2sqrt(6)x+2=0 .

Find the values of a for which all the roots of the euation x^4-4x^3-8x^2+a=0 are real.