If x+a is a common factor of expression `f(x)=x^(2)+px+q and g(x)=x^(2)+mx+n`, show that `a=(n-q)/(m-p)`.

If x ^(2) -3x+2 is a factor of x ^(4) -px ^(2) +q=0, then p+q=

If greatest common divisor of x^(3)-x^(2)+px - 7 and x^(2)-4x +q is (x-1) , then the value of p^(2)+q^(2) is

If x+3 is a factor of f(x)=px^(2)+p^(2)x+30 and pgt0 , what is the value of p?

If f: Q->Q ,\ \ g: Q->Q are two functions defined by f(x)=2x and g(x)=x+2 , show that f and g are bijective maps. Verify that (gof)^(-1)=f^(-1)\ og^(-1) .

IF x^2-3x +2 is a factor of x ^4 -px^2 +q=0 then (p,q)

If (x+2) is a common factor of (px^2+qx+r) and (qx^2+px+r) then (a) p=q or p+q+r=0 (b) p=r or p+q+r=0 (c) q=r or p+q+r=0 (d) p=q=-1/2r

Consider two quadratic expressions f(x) =ax^2+ bx + c and g (x)=ax^2+px+c,( a, b, c, p,q in R, b != p) such that their discriminants are equal. If f(x)= g(x) has a root x = alpha , then

Consider the functions f(x) and g(x), both defined from R rarrR and are defined as f(x)=2x-x^(2) and g(x)=x^(n) where n in N . If the area between f(x) and g(x) is 1/2, then the value of n is

Consider the functions f(x) and g(x), both defined from R rarrR and are defined as f(x)=2x-x^(2) and g(x)=x^(n) where n in N . If the area between f(x) and g(x) is 1/2, then the value of n is

If x^(2) - 3x + 2 is factor of x^(4) - px^(2) + q then 2q - p is equal to