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 : c dot`

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|Exercise Exercise 2.11|8 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Exercise 2.12|11 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Exercise 2.9|12 Videos

  • STRAIGHT LINES

    CENGAGE|Exercise JEE Advanced Previous Year|4 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE|Exercise Question Bank|12 Videos

Similar Questions

Explore conceptually related problems

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 are in GP , 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=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

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

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 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

The number of values of a for which equations x^3+a x+1=0a n d x^4+a x^2+1=0 have a common root is a. 0 b. 1 c. 2 d. Infinite

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 the equation x^2 + bx + ca = 0 and x^2 + cx + ab = 0 have a common root and b ne c , then prove that their roots will satisfy the equation x^2 + ax + bc = 0 .