Home
Class 12
MATHS
If a ,b ,c in R and equations a x^2+b x...

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 : cdot`

Text Solution

Verified by Experts

The correct Answer is:
`1:2:9`
Given equation are
`x^(2) + 2x + 9 = 0` (1)
and `ax^(2) + bx + c = 0 ` (2)
Clearly, roots of Eq. (1) are imaginary . Eqs (1) and (2) have a
common root which must be imaginary, hance, both the roots will
common.Thereofore, Eqs (1) and (2) are identical
`therefore (a)/(1) = (b)/(2) = (c)/(9) or a : b:c = 1: 2 : 9` .
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 2.11|8 Videos

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 2.12|11 Videos

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 2.9|12 Videos

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise ARCHIVES (NUMERICAL VALUE TYPE)|1 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE PUBLICATION|Exercise All Questions|291 Videos

Similar Questions

Explore conceptually related problems

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 a ,b ,c be the sides of A B C and equations a x^2+b x+c=0 and 5x^2+12x+13=0 have a common root, then find /_Cdot

If the equation x^2+ax+bc=0" and " x^2+bx+ca=0 have a common root, then a+b+c =

If a, b, c are in G.P. and the equation ax^(2) + 2bx + c = 0 and dx^(2) + 2ex + f = 0 have a common root, then show that (d)/(a), (e)/(b), (f)/(c ) are in A.P.

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

Find the condition if equations ax^2+bx+c =0 and x^2+2x+3 =0 have a common root. (a,b,cinR)

If a,b,c are in G.P., then the equations ax^2+2bx+c =0 and dx^2+2ex+f =0 have a common root if d/a,e/b,f/c are in

If the equations a x^2+b x+c=0 and x^3+3x^2+3x+2=0 have two common roots, then a) a=b=c b) a=b!=c c) a=-b=c d) a+b+c=3

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 a a n d bdot

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.