1GIVEN ANS IS ,(-3/4 , -3/5)
Value of k for which kx2 - 2kx + 3x - 6 is positive for exactly two integral values of x is..................
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4 Answers
1If we put k=-3/4 in the equation we do not get integral roots.....
341Obviously we need k<0. Then the quadratic will be positive for x lying between the two roots,
Now, the roots of this quadratic are x=2, x=-3/k.
We cannot have -3/k<2 as -3/k>0 and the only integral value that would be included would be x=1.
So, -3/k>2. That means the two integral values of x are x=3, x=4.
So the condition to be imposed is 4<-3/k<5.
Hence we obtain k>-3/4 and k<-3/5. i.e. k \in \left(-\frac{3}{4}, -\frac{3}{5} \right)