If the equations `x^2+""2x""+""3""=""0` and `a x^2+""b x""+""c""=""0,""a ,""b ,""c in R` , have a common root, then `a"":""b"":""c` is (1) 3 : 2 : 1 (2) 1 : 3 : 2 (3) 3 : 1 : 2 (4) 1 : 2 : 3

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 the quadratic equations, a x^2+2c x+b=0 and a 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 the equation ax^(2) + bx + c = 0 and 2x^(2) + 3x + 4 = 0 have a common root, then a : b : c

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

If a ,b ,c in R and equations a x^2+b x+c=0 and x^2+2x+3=0 have a common root, then find a : b : c

If the equations ax^2 + bx + c = 0 and x^3 + x - 2 = 0 have two common roots then show that 2a = 2b = c .

If x=1 is a common root of the equations a x^2+a x+3=0 and x^2+x+b=0 , then a b=

Find the condition on a , b ,c ,d such that equations 2a x^3+bx^2+c x+d=0 and 2ax^2+3b x+4c=0 have a common root.

If equations ax^(2)-bx+c=0 (where a,b,c epsilonR and a!=0 ) and x^(2)+2x+3=0 have a common root, then show that a:b:c=1:2:3

The quadratic equations x^2"-"6x""+""a""=""0""a n d""x^2"-"c x""+""6""=""0 have one root in common. The other roots of the first and second equations are integers in the ratio 4 : 3. Then the common root is (1) 1 (2) 4 (3) 3 (4) 2