e that both the roots Prove that both the roots ofthe equation (x (x-b) t (x-b)(x-cy t (x- c) (x-a 0 are alw ind the interval in which lies if (a2 t a-2) (a <1 for all x e R x 13. Find the value of for which 2x2 2N t 1) x (N+ 1) 0 may have one root less than root greater than a. ao Find the value ofm for which the quadratic equation x m (2 x -8)-15 0 has both roots p 16, Solve 5x 4 5 V(m2 5x 28) If(k -10) x (2k 2)x t (k+ 13) 0 has one root less than 2 and the other more than 5 18. Ifx is real, find the values of k for which t 2 is valid 3x2 2x 5 19 Determine the range of value ofx for which x2 2x 5

Explanation

`-2<(x^2+4x+1)/(x^2+x+1)<2`

`-1<(x^2+kx+1)/(x^2+x+1)`

`0<2+(x^2+kx+1)/(x^2+x+1)`

`0<(3x^2+(2+k)x+3)/(x^2+x+1)`

`3x^2+(2+k)x+3>0`

`(2+k)^2-4*3*2<0`

`(k+z)^2<36`

`-6ltk+2<6`

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