If `a_1x^2 + b_1 x + c_1 = 0` and `a_2x^2 + b_2 x + c_2 = 0 ` has a common root, then the common root is

IF x^2 + a x + bc = 0 and x^2 + b x + c a = 0 have a common root , then a + b+ c=

If a_1x^3 + b_1x² + c_1x + d_1 = 0 and a_2x^3 + b_2x^2+ c_2x + d_2 = 0 have a pair of repeated common roots, then prove that |[3a_1,2b_1,c_1],[3a_2,2b_2,c_2],[a_2b_1-a_1b_2,c_1a_2-c_2a_1,d_1a_2-d_2a_1]|=0

If a_1x^3 + b_1x² + c_1x + d_1 = 0 and a_2x^3 + b_2x^2+ c_2x + d_2 = 0 have a pair of repeated common roots, then prove that |[3a_1,2b_1,c_1],[3a_2,2b_2,c_2],[a_2b_1-a_1b_2,c_1a_2-c_2a_1,d_1a_2-d_2a_1]|=0

If a_1x^3 + b_1x² + c_1x + d_1 = 0 and a_2x^3 + b_2x^2+ c_2x + d_2 = 0 have a pair of repeated roots common, then prove that |[3a_1,2b_1,c_1],[3a_2,2b_2,c_2],[a_2b_1-a_1b_2,c_1a_2-c_2a_1,d_1a_2-d_2a_1]|=0

If a_1x^3 + b_1x² + c_1x + d_1 = 0 and a_2x^3 + b_2x^2+ c_2x + d_2 = 0 have a pair of repeated roots common, then prove that |[3a_1,2b_1,c_1],[3a_2,2b_2,c_2],[a_2b_1-a_1b_2,c_1a_2-c_2a_1,d_1a_2-d_2a_1]|=0

The equations x^(2)-2x+1=0,x^(2)-3x+2=0 have a common root then that common root is

If the equations ax^2 + bx + c = 0 and x^2 + x + 1= 0 has one common root then a : b : c is equal to

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 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+bc=0 and x^(2)+bx+ca=0 have a common root,then a+b+c=1