Question

Find the amount and the compound interest on rs 4000 in 2 years, if the rate if interest for the first year is 10 percent and for the second year is 15 percent

Answer 1

Answer:

compound interest = rs. 1060

Amount = rs. 5060

Step-by-step explanation:

c.i = p₁ (1+r₁/100) (1+r₂/100) - p₁

c.i = 4000 (1 + 10/100) (1 + 15/100) - 4000

c.i =(4000 * 110 * 115 /10000 ) - 4000

c.i = 50600000/10000 - 4000

c.i = 5060 - 4000

        { 5060 = amount [ ∵ p₁ (1 + r/100) = A. }

c.i = 1060

Answer 2

Answer:

Step-by-step explanation:

f(x) = kx³ – 8x² + 5

Roots are α – β , α & α +β

Sum of roots = – (-8)/k

Sum of roots = α – β + α + α +β = 3α

= 3α = 8/k

= k = 8/3α

or we can solve as below

f(x) = (x – (α – β)(x – α)(x – (α +β))

= (x – α)(x² – x(α+β + α – β) + (α² – β²))

= (x – α)(x² – 2xα + (α² – β²))

= x³ – 2x²α + x(α² – β²) – αx² +2α²x – α³ + αβ²

= x³ – 3αx² + x(3α² – β²) + αβ² – α³

= kx³ – 3αkx² + xk(3α² – β²) + k(αβ² – α³)

comparing with

kx³ – 8x² + 5

k(3α² – β²) = 0 => 3α² = β²

k(αβ² – α³) = 5

=k(3α³ – α³) = 5

= k2α³ = 5

3αk = 8 => k = 8/3α

(8/3α)2α³ = 5

=> α² = 15/16

=> α = √15 / 4