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Q.

The positive value of k for which the equation x 2  + kx + 64 = 0 and x 2  – 8x + k = 0 will both have real roots, is


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a

4

b

8

c

12

d

16 

answer is D.

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Detailed Solution

Given: The equations x 2 +kx+64=0   and x 2 8x+k=0   The quadratic equation of the form ax2+bx+c=0 have equal roots if the discriminant (D) is equal to zero.
We know,
D= b 2 4ac=0..(1)  
In x 2 +kx+64=0;a=1,b=k,c=64   Substitute the values in equation (1)
k 2 4×1×64=0  
k 2 256 =0 k 2 =256 k =±16...... (2)   
In x 2 8x+k=0;a=1,b=8,c=k   Substitute the values in equation (1)
(8) 2 4×1×k =0 644k =0 4k =64 k = 64 4 k =16.....(3)   Thus, from equation (2) and (3): k=16  
Therefore, the positive value of k for which the equation x 2 +kx+64=0   and x 2 8x+k=0   will both have real roots, is 16.
The correct answer is (4).
 
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The positive value of k for which the equation x 2  + kx + 64 = 0 and x 2  – 8x + k = 0 will both have real roots, is