Home
Class 12
MATHS
If a ,b ,c in R such that a+b+c=0a n da...

If `a ,b ,c in R` such that `a+b+c=0a n da!=c` , then prove that the roots of `(b+c-a)x^2+(c+a-b)x+(a+b-c)=0` are real and distinct.

Text Solution

Verified by Experts

Given equation is
`(b + c - a)^(2) + ( c + a - b) x + ( a + b - c) = 0`
or `(-2a)x^(2) + (-2b)x + (-2c) = 0`
or `ax^(2) + bx + c = 0`
`rArr D = b^(2) - 4ac`
`= (-c - a)^(2) - 4ac`
`= (c - a)^(2) gt 0`
Hence, roots are real and distinct
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Exercise 2.9|12 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Exercise 2.10|5 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Exercise 2.7|9 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 in R such that a+b+c=0 and a!=c, then prove that the roots of (c+a-b)x+(a+b-c)=0 are real and distinct.

If a,b,c in R such that a+b+c=0 and a is not equal to c, then the roots of (b+c-a)x^(2)+(c+a-b)x+(a+b-c)=0

If a+b+c=0 and a,b,c are ratiional. Prove that the roots of the equation (b+c-a)x^(2)+(c+a-b)x+(a+b-c)=0 are rational.

If a + b + c = 0 and a ne c then the roots of the equation (b + c - a)x^(2) + (c + a - b)x + (a + b - c) = 0 , are

If a,b,c in Q, then roots of the equation (b+c-2a)x^(2)+(c+a-2b)x+(a+b-2c)=0 are