Roots of the equation (a+b-c) x2-2 a x+(a-b+c)=0,(a, b, c ∈ Q) are-

Question

Roots of the equation (a+b-c) x2-2 a x+(a-b+c)=0,(a, b, c ∈ Q) are- (A) rational (B) irrational (C) complex (D) can't be determine

Tardigrade Admin · Accepted Answer

D=4 a2-4[a-b+c](a+b-c) =4[a2- a2+a b-a c-a b-b2+b c+a c+b c-c2]. =4[b2+c2-2 b c]=4(b-c)2 D= 2(b-c) 2 Hence D is perfect square of a rational number Hence (1)

Q. Roots of the equation $(a + b - c) x^{2} - 2 a x + (a - b + c) = 0, (a, b, c \in Q)$ are-

rational

irrational

complex

can't be determine

$D = 4 a^{2} - 4 [a - b + c] (a + b - c)$
$= 4 [a^{2} - {a^{2} + ab - a c - ab - b^{2} + b c + a c + b c - c^{2}]$
$= 4 [b^{2} + c^{2} - 2 b c] = 4 (b - c)^{2}$
$D = {2 (b - c)}^{2}$
Hence D is perfect square of a rational number
Hence (1)

Q. Roots of the equation (a+b−c)x2−2ax+(a−b+c)=0,(a,b,c∈Q) are-