V=
-7
.: p(x) = 2x+ +5.2.3 - 3x2 – 72 +3
= (2x + 3)(x - 1)(x2 + 2x - 1)
2
-=-1
now 22 + 2x - 1 has zeros -21 4–4()
202 = -2=212
-2
.: p(x) has zeros - , 1, and -15v2.
7 a (2x+1) and (2-2) are factors of p(z) = 2x4 + ax3 + b2 19
find constants a and b, and all zeros of p(x).
b (x+3) and (2x - 1) are factors of 2r+ + ax + bx² + ax +3.
find constants a and b, and hence determine all zeros of the quartic.
8 find k given that 42+ - 4x + kr- 63 +9 is a perfect square.
9 write 24 - 228 - 3.x2 + 4x +3 in the form a(r? - 2)2 + b(x2 - 1) +
are constants.
henco find all