Question

show that the roots of the equation x-- 2m + -
the roots of the equation a (b - c) x2 + b(c - a) x + c (a - b) = 0 are equal, show that
real values of p.
x + 3 = 0 are real for all (non-zero) real
m
values of m.

Answer 1

Step-by-step explanation:

ANSWER

As we know that for the quadratic equation ax

2

+bx+c=0, roots will be equal if

D=B

2

−4AC=0

Therefore, for the equation,

a(b−c)x

2

+b(c−a)x+c(a−b)=0

A=a(b−c),B=b(c−a),C=c(a−b)

D=0

B

2

−4AC=0

(b(c−a))

2

−4(a(b−c))(c(a−b))=0

⇒ab+bc=2ac

Hence a,b and c are in HP.