If the quadratic equations x^2+bx+ca=0 &...

If the quadratic equations `x^2+bx+ca=0 & x^2+cx+ab=0` (where `a!= 0`) have a common root. prove that the equation containing their other root is `x^2+ax+bc=0`

AI Generated Solution

Similar Questions

Explore conceptually related problems

Root of the quadratic equation x^2+6x-2=0

If the quadratic equations x^(2) +pqx +r=0 and z^(2) +prx +q=0 have a common root then the equation containing their other roots is/are

lf the quadratic equations x^2+bx+c=0 and bx^2+cx+1=0 have a common root then prove that either b+c+1=0 or b^2+c^2+1=bc+b+c .

If x^2+a x+bc=0 a n d x^2+b x+c a=0(a!=b) have a common root, then prove that their other roots satisfy the equation x^2+c x+a b=0.

If a,b,c, in R and equations ax^(2) + bx + c =0 and x^(2) + 2x + 9 = 0 have a common root then

If the quadratic equation ax^(2) + 2cx + b = 0 and ax^(2) + 2x + c = 0 ( b != c ) have a common root then a + 4b + 4c is equal to

The quadratic equation ax^(2)+bx+c=0 has real roots if:

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

If x^2+a x+b=0a n dx^2+b x+c a=0(a!=b) have a common root, then prove that their other roots satisfy the equation x^2+c x+a b=0.

If the equation ax^2+2bx+c=0 and ax^2+2cx+b=0 b!=c have a common root ,then a/(b+c =