Home
Class 12
MATHS
If a ,b ,c be the sides of A B C and eq...

If `a ,b ,c` be the sides of ` A B C` and equations `a x 62+b x+c=0a n d5x^2+12+13=0` have a common root, then find `/_Cdot`

Text Solution

Verified by Experts

The correct Answer is:
`angle C = 90^(@)`
Roots of equation `5x^(2) + 12 x + 13 = 0` are imaginary
Hence, both equation have same roots
`therefore a : b:c = 5 :12: 13`
`therefore a = 5k , b = 12k , c = 13k `
Here `c^(2) = a^(2) + b^(2) `
`rArr angle C = 90^(@)`
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|20 Videos

Similar Questions

Explore conceptually related problems

If a,b,c be the sides of ABC and equations ax^(2)+bx+c=0and5x^(2)+12+13=0 have a common root,then find /_C.

If a,b,c denote the sides of a !ABC and the equations ax^(2)+bx+c=0 and x^(2)+sqrt2x+1=0 have a common root, then ""^(@)C=

If a,b,c in R and the equation ax^(2)+bx+c=0 and x^(2)+x+1=0 have a common root,then

If the equations ax^(2)+bx+C=0 and x^(2)+2x+4=0 have a common root then find a:b:c

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

If a , b , c denote the sides of a !ABC such that the equation x^(2)+sqrt2x+1=0 and ax^(2)+bx+c=0 have a common root , then C =

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