Question

Solve this as fast as possible....itz urgent...

Answer 1

(k+1)x² - 12x + 2k-1

D = b² - 4ac

D = 144 - 4(k+1)(2k-1)

D = 144 - 4(2k² - k + 2k - 1)

D = 144 - 8k² + 4k - 8k + 4

D = -8k² - 4k + 148

0 = -2k² - k + 37 [ For solutions ]

2k² + k - 37 = 0

k² + k/2 - 37/2 = 0

k² + k×1/4×2 - 37/2 = 0

k² + k×1/4×2 + (1/4)² - (1/4)² - 37/2 = 0

(k + 1/4)² - 1/16 - 37/2 = 0

(k + 1/4)² = 1/16 + 37/2

(k + 1/4)² = (2 + 592)/32

(k + 1/4)² = 594/32

(k + 1/4)² = 297/16

√(k+1/4)² = ±√297/4

k = √297/4 - 1/4 or - √297/4 - 1/4

k = (√297 - 1)/4 or -(√297 + 1)/4

[ k = (√297 - 1)/4 or -(√297+1)/4 ]

=> (k+1)x² - 12x + (2k - 1)

=> ((√297-1)/4 + 1)x² - 12x + (2×(√297 - 1)/4 - 1)

=> ((√297 - 1 + 4)/4)x² - 12x + ((√297-1-2)/2)

=> ((√297 - 3)/4)x² - 12x + √297-3/2

Equation formed

$\frac{ \sqrt{297} - 3 }{4} {x}^{2} - 12x + \frac{ \sqrt{297} - 3 }{2}$

Multiplying the whole equation by 2 , we get

$\frac{ \sqrt{297} - 3}{2} {x}^{2} - 24x + \sqrt{297} - 3$