Theory question 109
Polynomials(a) If (x + 2) is a factor of g(x) = 2x3 + 11x2 − x − 30, find the zeros of g(x).
(b) Solve 3(2x) + 3y−2 = 25 and 2x − 3y+1 = −19 simultaneously.
Show the model answer
Model answer
(a) g(x) = (x + 2)(2x² + 7x − 15) = (x + 2)(2x − 3)(x + 5). Zeros: −2, 3/2, −5.
(b) Let a = 2ˣ, b = 3ʸ: 3a + b/9 = 25 and a − 3b = −19.
a = 3b − 19, so 9b − 57 + b/9 = 25, 82b/9 = 82, b = 9 and a = 8.
x = 3, y = 2.
Explanation
Substitute a = 2ˣ and b = 3ʸ to get ordinary simultaneous equations.