Question

Statement-1:  ax² + bx + C = 0 is a quadratic equation with real coefficients, if 2 + 3 is one root then other root can be any other real number.

Statement-2: If P + √q + is a real root of a quadratic equation, then P - √q is other root only when the coefficients of equation are rational

(A) Statement – 1 is True, Statement – 2 is True; Statement – 2 is a correct explanation for Statement – 1. 

(B) Statement – 1 is True, Statement – 2 is True; Statement – 2 is NOT a correct explanation for Statement – 1.

(C) Statement – 1 is True, Statement – 2 is False. 

(D) Statement – 1 is False, Statement – 2 is True

Answer 1

 Correct option (D) Statement – 1 is False, Statement – 2 is True

Explanation:

R is obviously true. So test the statement let f(x) = (x – p) (x – r) + λ (x – q) (x – s) = 0

 Then f(p) = λ (p – q) (p – s) f(r) = λ (r – q) (r – s) If λ > 0 then f(p) > 0, f(r) < 0

⇒ There is a root between p & r Thus statement-1 is false.