If `a ,b ,c` be the sides of ` A B C` and equations `a x^2+b x+c=0a n d5x^2+12x+13=0` have a common root, then find `/_Cdot`

If a ,b ,c in R and equations a x^2+b x+c=0a n dx^2+2x+9=0 have a common a rot, then find a : b : c dot

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 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

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=

a ,b ,c are positive real numbers forming a G.P. ILf a x 62+2b x+c=0a n ddx^2+2e x+f=0 have a common root, then prove that d//a ,e//b ,f//c are in A.P.

The value of b for which the equation x^2+bx-1=0 and x^2+x+b=0 have one root in common is

If equations x^2+a x+12=0. x^2+b x+15=0a n dx^2+(a+b)x+36=0, have a common positive root, then find the values of aa n dbdot

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

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 equations a x^2+b x+c=0a n dx^3+3x^2+3x+2=0 have two common roots, then a. a=b=c b. a=b!=c c. a=-b=c d. none of these