The positive value of ‘k’ for which x2+kx+64=0 and x2-8x+k=0 will both have real roots is

a) 8 b) 4 c) 12 d) 16

 

 

 

Asked by arajeevshashank | 30th Jun, 2020, 05:00: PM

Expert Answer:

Given quadratic equations are
(i) x2 + kx + 64 = 0
(ii) x2 - 8x + k = 0
The equations has real roots when the discriminant is greater than or equal to 0.
rightwards double arrow D equals b squared minus 4 a c greater or equal than 0
F o r space q u a d r a t i c space e q u a t i o n space left parenthesis i right parenthesis
open parentheses k close parentheses squared minus 4 cross times 1 cross times 64 greater or equal than 0
k squared minus 256 greater or equal than 0
k squared minus 16 squared greater or equal than 0
left parenthesis k minus 16 right parenthesis left parenthesis k plus 16 right parenthesis greater or equal than 0
k minus 16 greater or equal than 0 space a n d space k plus 16 greater or equal than 0 space space O R thin space space k minus 16 less or equal than 0 space a n d space k plus 16 less or equal than 0
k greater or equal than 16 space a n d space k greater or equal than negative 16 space space O R space space k less or equal than 16 space a n d space k less or equal than negative 16
rightwards double arrow k greater or equal than 16 space space O R thin space space k less or equal than negative 16
rightwards double arrow k element of left parenthesis negative infinity comma space minus 16 right square bracket space union space left square bracket 16 comma space infinity right parenthesis
P o s i t i v e space v a l u e s space k space a r e space left square bracket 16 comma space infinity right parenthesis.

F o r space q u a d r a t i c space e q u a t i o n space left parenthesis i right parenthesis
open parentheses negative 8 close parentheses squared minus 4 cross times 1 cross times k greater or equal than 0
64 minus 4 k greater or equal than 0
16 minus k greater or equal than 0
16 greater or equal than k
rightwards double arrow k less or equal than 16 space
rightwards double arrow k element of left parenthesis negative infinity comma space 16 right square bracket
P o s i t i v e space v a l u e s space k space a r e space left square bracket 0 comma space 16 right square bracket.

P o s i t i v e space v a l u e space o f space k space f o r space left parenthesis i right parenthesis space a n d space left parenthesis i i right parenthesis space i s space 16.

Answered by Renu Varma | 1st Jul, 2020, 12:59: PM