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Question: For real values of x, the expression \(\frac{(x - b)(x - c)}{x - a}\) will assume all real values pr...

For real values of x, the expression (x−b)(x−c)x−a\frac{(x - b)(x - c)}{x - a} will assume all real values provided -

A

a £ c £ b

B

b ³ a ³ c

C

b £ c £ a

D

a ³ b ³ c

Answer

b ³ a ³ c

Explanation

Solution

y = x2−(b+c)x+bc(x−a)\frac{x^{2} - (b + c)x + bc}{(x - a)}

Ž x2 – (b + c + y) x + bc + ay – 0

D ³ 0

Ž (b + c + y)2 –4 (bc + ay) ³ 0

Ž y2 + 2(b + c – 2a) y + (b – c)2 ³ 0

D £ 0

Ž 4(b + c – 2a)2 – 4 (b – c)2 £ 0

Ž (2b – 2a) (2c – 2a) £ 0

Ž (a – b) (a – c) £ 0

Ž b £ a £ c if (b < c) or (c £ a £ b) if (c < b)