If `ax^(2)+ bx +c and bx ^(2) + ax + c` have a common factor `x +1` then show that `c=0 and a =b.`

If ax^2 + bx + c = 0 and bx^2 + cx+a= 0 have a common root and a!=0 then (a^3+b^3+c^3)/(abc) is

If the equation x^2+2x+3=0 and ax^2+bx+c=0 have a common root then a:b:c is

If (x ^(2) -1) is a factor of ax ^(4) + bx ^(3) + cx ^(2) + dx +e, then show that a + c +e =d +d=0

If a, b, c are in GP , then the equations ax^2 +2bx+c = 0 and dx^2 +2ex+f =0 have a common root if d/a , e/b , f/c are in

If ax + by = a^(2)-b^(2) and bx + ay = 0, find the value of x + y .

If the quadratic equations, a x^2+2c x+b=0a n da x^2+2b x+c=0(b!=c) have a common root, then a+4b+4c is equal to: a. -2 b. -2 c. 0 d. 1

If |ax^2 + bx+c|<=1 for all x is [0, 1] ,then

If ax^3 + bx^2 + cx + d is divisible by ax^2 + c , then a, b, c, d are in

ax^2 + bx + c = 0(a > 0), has two roots alpha and beta such alpha 2, then

If c gt0 and 4a+clt2b then ax^(2)-bx+c=0 has a root in the interval