CBSE Class 10 Answered

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 | 30 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 | 01 Jul, 2020, 12:59: PM

CBSE Class 10 Answered

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CBSE Class 10 Answered

Application Videos

Nature of Roots

Determining roots and nature of roots using discriminan ...

Quadratic Equation Equal Roots

Concept Videos

Concept of discriminant to classify roots of quadratic ...

Nature of Roots

Nature of Roots

Quadratic Equations

D = 0

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