The complete st of values for K,for which the quaratic equation x squared minus k x plus k plus 2 equals 0 has real roots,consists of-
a.2 plus square root of 12 space end root space space space b.2 root index plus minus of 12 space space c.2 minus square root of 12 space space space d. minus 2 minus square root of 2

Asked by Aastha | 4th Sep, 2014, 12:33: AM

Expert Answer:

T h e space q u a d r a t i c space e q u a t i o n space a x squared plus b x plus c equals 0 space h a s space r e a l space r o o t s space i f space b squared minus 4 a c greater than 0.  T h e space g i v e n space e q u a t i o n space i s space x squared minus k x plus k plus 2 equals 0  C o m p a r i n g space t h e space c o e f f i c i e n t s comma space w e space h a v e comma a equals 1 comma space b equals minus k space a n d space c equals k plus 2 T h u s comma space t h e space c o n d i t i o n space b squared minus 4 a c greater than 0 space b e c o m e s comma open parentheses minus k close parentheses squared minus 4 cross times 1 cross times open parentheses k plus 2 close parentheses greater than 0 rightwards double arrow k squared minus 4 k minus 8 greater than 0 rightwards double arrow k squared minus 4 k greater than 8 rightwards double arrow k squared minus 4 k plus 4 greater than 8 plus 4 rightwards double arrow k squared minus 4 k plus 4 greater than 12 rightwards double arrow open parentheses k minus 2 close parentheses squared greater than 12 rightwards double arrow open parentheses k minus 2 close parentheses greater than plus-or-minus square root of 12 rightwards double arrow open parentheses k minus 2 close parentheses plus 2 greater than 2 plus-or-minus square root of 12 rightwards double arrow k plus 2 greater than 2 plus-or-minus square root of 12 H e n c e space t h e space c o r r e c t space o p t i o n space i s space left parenthesis b right parenthesis.

Answered by Vimala Ramamurthy | 4th Sep, 2014, 10:02: AM