The graphs of `y=2x^(2)` and `y=ax + b` intersect at `x=2` and `6` ,then the quadratic equation in `x` , whose roots are `a+2` and `(b)/(4)-1` is

If alpha and beta are the roots of x^(2)-x-2=0 , find the quadratic equation in x whose roots are (2alpha+1) and (2beta+1):

The graph of the equation y=2x^(2)-3x+1 intersect the line y=0 at

If x^(2) - 3x + 2 is a factor of x^(4) - ax^(2) + b then the equation whose roots are a and b is

If x_(1) and x_(2) are the arithmetic and harmonic means of the roots fo the equation ax^(2)+bx+c=0 , the quadratic equation whose roots are x_(1) and x_(2) is

If x_(1) and x_(2) are roots of the quadratic equation 2x^(2)+3x-4=0, then find the quadratic equation whose roots are (2x_(1)+3)^(-2) and (2x_(2)+3)^(-2)

If x_(1) and x_(2) are roots of the quadratic equation x^(2)+x+4=0, then the quadratic equation whose roots are y_(k)=x_(k)+(1)/(x_(k)) where k=1,2, is :

If tan A&tan B are the roots of the quadratic equation x^(2)-ax+b=0 ,then the value of sin^(2)(A+B) is: