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

Application Videos

This video explains the concept of Discriminant and Nature of Roots.

Concept Videos

Understand the concept of discriminant to classify roots of quadratic equat...

This video explains the concept of discriminant to classify roots of quadra...

This video explains the concept of discriminant to classify roots of quadra...

Nature of Roots

Quadratic Equations, Nature of Roots

This video covers an application on nature of roots

Practice Test

Webinar

Pre Board Assessment
All Questions Ask Doubt