Apakah nilai k?

Jawapan:

Jawapannya ialah #k dalam (2,4) #

Penjelasan:

Untuk persamaan kuadratik #f (x)> 0 #, graf mesti menyentuh paksi-x

Diskriminasi mestilah #=0#

#f (x) = x ^ 2-2 (4k-1) x + 15k ^ 2-2k-7 #

# Delta = (2 (4k-1)) ^ 2-4 (1) (15k ^ 2-2k-7) = 0 #

#=>#, # 4 (16k ^ 2-8k + 1) -60k ^ 2 + 8k + 28 = 0 #

#=>#, # 64k ^ 2-32k + 4-60k ^ 2 + 8k + 28 = 0 #

#=>#, # 4k ^ 2-24k + 32 = 0 #

#=>#, # 4 (k ^ 2-6k + 8) = 0 #

#=>#, # (k-2) (k-4) = 0 #

#=>#, # {(k = 2), (k = 4):} #

Bila # k = 2 #

#=>#, # x ^ 2-14x + 49 = 0 #

graf {x ^ 2-14x + 49 -14.48, 21.55, -4.62, 13.4}

Bila # k = 4 #

#=>#, # x ^ 2-30x + 225 = 0 #

graf {x ^ 2-30x + 225 -14.48, 21.55, -4.62, 13.4}

Bila # k = 3 #

#=>#, # x ^ 2-22x + 122 = 0 #

graf {x ^ 2-22x + 122 -14.48, 21.55, -4.62, 13.4}