For `a ne b`, if the equation `x^(2)+ax+b=0" and "x^(2)+bx+a=0` have a common root, then the value of a+b=

If the equations 2x^(2)-7x+1=0 and ax^(2)+bx+2=0 have a common root, then

If the equation x^(3)+k x^(2)+3=0 and x^(2)+k x+3=0 have a common root, then the value k .

If the quadratic equations 3 x^(2)+a x+1=0 and 2 x^(2)+b x+1=0 have a common root, then the value of the expression 5 a b-2 a^(2)-3 b^(2) is

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

If x^(2)+ax+10=0" and "x^(2)+bx-10=0 have a common root, then a^(2)-b^(2) is equal to

If the equation x^2+b x-a=0"and" x^2-a x+b=0 have a common root, then a. a+b=0 b. a=b c. a-b=1 d. a+b=1

If a, b, c are positive real numbers such that the equations ax^(2) + bx + c = 0 and bx^(2) + cx + a = 0 , have a common root, then

If the equation x^2 + bx + ca = 0 and x^2 + cx + ab = 0 have a common root and b ne c , then prove that their roots will satisfy the equation x^2 + ax + bc = 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