Set of values of ' K ' for which roots of the quadratic x2-(2 K-1) x+K(K-1)=0 are -

Question

Set of values of ' K ' for which roots of the quadratic x2-(2 K-1) x+K(K-1)=0 are - (A) both less than 2 is K ∈(2, ∞) (B) of opposite sign is K ∈(-∞, 0) ∪(1, ∞) (C) of same sign is K ∈(-∞, 0) bigcup(1, ∞) (D) both greater than 2 is K ∈(2, ∞)

Tardigrade Admin · Accepted Answer

(A)

Expression is ( x 2+( K + K -1) x + K ( K -1)=0. ⇒ (x-K)(x-K+1)=0 ⇒ x=K text or x=K-1 ⇒ text greater part < 2 ⇒ K< 2 (B) Opposite sign (( c / a )<0) ⇒ K ( K -1)<0 ⇒ K ∈(0,1) (C) K ( K -1) >0 ⇒ K ∈(-∞, 0) ∪(1, ∞) (D) K -1 >2 ⇒ K >3 ⇒ K ∈(3, ∞)

Q. Set of values of ' $K$ ' for which roots of the quadratic $x^{2} - (2 K - 1) x + K (K - 1) = 0$ are -

both less than 2 is $K \in (2, \infty)$

of opposite sign is $K \in (- \infty, 0) \cup (1, \infty)$

of same sign is $K \in (- \infty, 0) ⋃ (1, \infty)$

both greater than 2 is $K \in (2, \infty)$

Q. Set of values of ' K ' for which roots of the quadratic x2−(2K−1)x+K(K−1)=0 are -

both less than 2 is K∈(2,∞)

of opposite sign is K∈(−∞,0)∪(1,∞)

of same sign is K∈(−∞,0)⋃(1,∞)

both greater than 2 is K∈(2,∞)

(A) Expression is (x2+(K+K−1)x+K(K−1)=0 ⇒(x−K)(x−K+1)=0 ⇒x=K or x=K−1 ⇒ greater part <2⇒K<2 (B) Opposite sign (ac​<0)⇒K(K−1)<0 ⇒K∈(0,1) (C) K(K−1)>0⇒K∈(−∞,0)∪(1,∞) (D) K−1>2⇒K>3⇒K∈(3,∞)

Q. Set of values of ' $K$ ' for which roots of the quadratic $x^{2} - (2 K - 1) x + K (K - 1) = 0$ are -

both less than 2 is $K \in (2, \infty)$

of opposite sign is $K \in (- \infty, 0) \cup (1, \infty)$

of same sign is $K \in (- \infty, 0) ⋃ (1, \infty)$

both greater than 2 is $K \in (2, \infty)$