If `tan A` and `tan B` are the roots of the quadratic equation `x^2-px + q =0` then value of `sin^2(A+B)`

If tanA and tanB the roots of the quadratic equation, 4x^(2)-7x+1=0 then evaluate 4sin^(2)(A+B)-7sin(A+B)*cos(A+B)+cos^(2)(A+B) .

If the roots of the quadratic equation x^2 - ax + 2b = 0 are prime numbers, then the value of (a-b) is

If tan alpha tan beta are the roots of the equation x^2 + px +q =0(p!=0) then

If alpha and beta are the roots of the quadratic equation x^(2) + px + q = 0 , then form the quadratic equation whose roots are alpha + (1)/(beta), beta + (1)/(alpha)

If p and q are roots of the quadratic equation x^(2) + mx + m^(2) + a = 0 , then the value of p^(2) + q^(2) + pq , is

If the roots of the quadratic equation x^(2)+px+q=0 are tan 30^(@) and tan15^(@) , then value of 2+q-p is

Let a,b,c,d be distinct real numbers and a and b are the roots of the quadratic equation x^2-2cx-5d=0 . If c and d are the roots of the quadratic equation x^2-2ax-5b=0 then find the numerical value of a+b+c+d .

Q. If tan alpha and tan beta are the roots of equation x^2-12x-3=0 , then the value of sin^2(alpha+beta)+2sin(alpha+beta)cos(alpha+beta)+5cos^2(alpha+beta) is

If sin theta and cos theta are the roots of the quadratic equation ax ^(2) +bx + c=0(a ne 0). Then find the value of (b ^(2) -a^(2))/(ac ).