Q. 324.9( 7 Votes )

The values of k f

Answer :

Given: 16x2 + 4kx + 9 = 0
To find:The values of k for which the quadratic equation 16x2 + 4kx + 9 = 0 has real and equal roots.
Solution:
To have real and equal roots d = 0
Where d=b2 – 4ac

⇒b2 – 4ac = 0
Compare with the general equation of quadratic equation ax2 + bx + c = 0, a≠0

here a = 16, b = 4k and c = 9


⇒b2 – 4ac =(4k)2 – 4 x 16 x 9 = 0


⇒16 k2 – 576 = 0


⇒k2 = 576 /16


⇒k = 24/ 4


k = ±6

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