Theory question 107
Quadratic Equations(a) Solve, correct to two decimal places, the equation 4x2 = 11x + 21.
(b) A man invests £1500 for two years at compound interest. After one year, his money amounts to £1560. Find the: (i) rate of interest; (ii) interest for the second year.
(c) A car costs ₦300,000.00. It depreciates by 25% in the first year and 20% in the second year. Find its value after 2 years.
Show the model answer
(a) 4x2 − 11x − 21 = 0. x = [11 ± √(121 + 336)]/8 = (11 ± √457)/8 = (11 ± 21.378)/8.
x ≈ 4.05 or x ≈ −1.30.
(b)(i) Interest in year 1 = £60; rate = 60/1500 × 100% = 4%.
(ii) Compound interest: second-year interest = 4% of £1560 = £62.40.
(c) After year 1: 300,000 × 0.75 = ₦225,000. After year 2: 225,000 × 0.80 = ₦180,000.00.
With compound interest the second year's interest is on the new amount, £1560.