Q no 7: 7 The subset of complete set of values of k for which the expression - Maths -

Question

Q no 7:

7 The subset of complete set of values of k for which the
expression x2-2(k-2) x-2k2-5k+6 is always
positive is

A   - 1 , 2 3              
        B   0 , 1 2      
          C   ( - ∞ ,   -
1 ]   ∪ [ 2 3 ,   ∞ ) ,      
              D   2 3 , 1

Lovina Kansal · Accepted Answer

Dear student We have,x2-2(k-2)x-2k2-5k+6Consider D=b2-4ac>0⇒-2(k-2)2-4(1)(-2k2-5k+6)>0⇒4(k2+4-4k)-4(-2k2-5k+6)>0⇒4k2+16-16k+8k2+20k-24>0⇒12k2+4k-8>0⇒3k2+k-2>0⇒k-23k+1>0 x<-1 x=-1 -123 x-23 - - - 0 + x+1 - 0 + + + x-23x+1 + 0 - 0 + Combine the ranges that satisfy the required condition:>0x<-1 or x>23⇒x∈-∞,-1∪23,∞ Regards

	x<-1	x=-1	$- 1 < x < \frac{2}{3}$	$x = \frac{2}{3}$	$x > \frac{2}{3}$
$x - \frac{2}{3}$	-	-	-	0	+
x+1	-	0	+	+	+
$(x - \frac{2}{3}) (x + 1)$	+	0	-	0	+

Q no. 7: 7. The subset of complete set of values of k for which the expression x2-2(k-2) x-2k2-5k+6 is always positive is. A - 1 , 2 3 B 0 , 1 2 C ( - ∞ , - 1 ] ∪ [ 2 3 , ∞ ) , D 2 3 , 1

Q no. 7:

7. The subset of complete set of values of k for which the expression x²-2(k-2) x-2k²-5k+6 is always positive is.

$(A) (- 1, \frac{2}{3}) (B) (0, \frac{1}{2}) (C) (- \infty, - 1] \cup [\frac{2}{3}, \infty), (D) (\frac{2}{3}, 1)$