Theory of Equations 5 Question 17

17. If a<b<c<d, then the roots of the equation (x−a) (x−c)+2(x−b)(x−d)=0 are real and distinct.

(1984, 1M)

Analytical & Descriptive Question

Show Answer

Answer:

Correct Answer: 17. (True)

Solution:

  1. Let f(x)=(x−a)(x−c)+2(x−b)(x−d)

Here,

f(a)=+vef(b)=−vef(c)=−vef(d)=+ve

∴ There exists two real and distinct roots one in the interval (a,b) and other in (c,d).

Hence, statement is true.

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