Q12 of 109 Page 3

If zeros of the polynomial f (x) = x3 – 3px2 + qx – r are in A.P., then

Given;


f(x) = x3 – 3px2 + qx – r


Let a, b and c be the zeroes of the polynomial x3 – 3px2 + qx – r


a + b + c = 3 p


ab + bc + ac = q


abc = r


a + b = 2b ⇒ b = p ⇒ a + c = 2p


b(a + c) + ac = q


⇒ 2p2 + ac = q


⇒ ac = r/p


∴ 2p2 + r/p = q


2p3 = pq – r

More from this chapter

All 109 →
10

Figure 2.23 shows the graph of the polynomial f(x) = ax2 + bx + c for which

 11

If the product of zeros of the polynomial f(x) = ax3 –6x2 + 11x – 6 is 4, then a =

 13

If the product of two zeros of the polynomial f (x) = 2xZ3 + 6x2 – 4x + 9 is 3, then its third zero is

 14

If the polynomial f(x) = ax3 + bx – c is divisible by the polynomial g(x) = x2 + bx + c, then ab =