If 4 < x < 8 then the value of 12x-x²-32 is

I:If α,β are the roots of the equation ax²+bx+c=0 then the quadratic equation whose roots are α+β,αβ is a²x²+a(b-c)x-bc=0

II:If α,β are the roots of 9x²+6x+1=0 then the equations with the roots 1/α,1/β is x²+6x+9=0

The maximum value of a²-abx-b²x² is

The value of ‘a’ such that the sum of cubes of the roots of the equation x² – ax + (2a – 3)=0 assumes the minimum value is

The extreme value of x²-5x+6 is

If x²+4y²-8x+12=0 is satisfied by real values of x and y then y must lies between

If xy+2x-3y-k is resolvable into two linear factors then k=

The number having two digits such that it is 4 times the sum and three times the product of its two digits are

If x²+ky²+x-y is resolvable into two linear factors then k=

x²-2x+10 has minimum at x=