Theory question 110
Polynomials(a) Find the range of values of p for which 4x2 − px + 1 = 0 has real roots. (b)(i) Expand (1 + 3xy)6 in assending powers of x. (ii) Using the expansion in 10(b)(i), find, correct to four significant figures, the value of (1.03)6.
Show the model answer
Model answer
(a) p² − 16 ≥ 0, so p ≤ −4 or p ≥ 4.
(b)(i) 1 + 18xy + 135x²y² + 540x³y³ + 1215x⁴y⁴ + 1458x⁵y⁵ + 729x⁶y⁶.
(ii) 3xy = 0.03, so xy = 0.01: 1 + 0.18 + 0.0135 + 0.00054 + 0.0000122 + … ≈ 1.194.
Explanation
Choose xy so that 1 + 3xy = 1.03.