Given that x 2+2kx+4k-3 = 0 has no real roots, show that k satisfies k
2
-4k+3 < 0

for unreal roots: b² < 4ac

• b is 2k

• a is 0

• c is 4k - 1

34.5 cm

step-by-step explanation:

generally for a circular segment of angle, θ° and radius r

arc length

= (θ/360) x circumference

= (θ/360) x 2πr

in our case, θ = 60°, π=3.142 and r = 33 cm

substitute into above formula

arc length

= (60/360) x 2(3.142)( 33) = 34.5 cm

= 5

step-by-step explanation:

to find the 15th term substitute n = 15 into the nth term formula

= (- 3 × 15 ) + 50 = - 45 + 50 = 5