The quadratic equations x² – 6xa = 0 and x² – cx + 6 = 0 and have one root in common. The other roots of the first and second equations are integers in the ratio 4 : 3. Then the common root is

3x-5x²+12 has maximum at x=

The cost of a cloth piece is Rs.35/-.If the length of the cloth piece is 4 metres more and each metre costs Rs.1/- less,the cost would remain unchanged.The length of the cloth piece is

If x²-y²+4x-6y+k is resolvable into two linear factors then k=

The expression x²-5x-6 is negative if x lies in

If one root of the equation ax²+bx+c=0 is equal to the n^th power of the other then (acⁿ)^1/n+1+(aⁿc)^1/n+1+b=

If the sum of the roots of the equation 5x²-4x+2+k(4x²-2x-1)=0 is 6,then k=

The least integral value of x for which 33-x(2+3x)>0 is

If the tangent  at the point  P (2,4) to the parabola y²= 4ax meets the parabola y²= 8x + 5 at Q and R, then the midpoint of QR is