Home
Class 12
MATHS
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`

Promotional Banner

Similar Questions

Explore conceptually related problems

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

If the quadratic equation ax^(2)+2cx+b=0 and ax^(2)+2bx+c=0(b!=c) have a common root,then a+4b+4c=

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

If the quadratic equation x^(2) +ax +b =0 and x^(2) +bx +a =0 (a ne b) have a common root, the find the numeical value of a +b.

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 equations x^(2)+abx+c=0 and x^(2)+acx+b=0 have a common root,then their other roots satisfy the equation

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

If 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