Q3 of 16 Page 150

Find polynomials p(x) satisfying each set of conditions below.

Three different second degree polynomials with p(0) = 0 and p(1) = 2.

Let an arbitrary polynomial be p(x)


p(x) = ax2 + bx + c


⇒ p(0) = c = 0


⇒ p(1) = a + b = 1


⇒ p(x) = ax2 + bx (where a + b = 1)


There could be infinite number of such polynomials but we have to find only 3.





They are any three possible polynomials.


More from this chapter

All 16 →
3

Find polynomials p(x) satisfying each set of conditions below.

First degree polynomial with p(1) = –1 and p(–2) = 3.

 3

Find polynomials p(x) satisfying each set of conditions below.

Second degree polynomial with p(0) = 0, p(1) = 2 and p(2) = 6.

 1

Taking p(x) = 2x2 + 3x + 5, q(x) = x2 + 4x + 1 and s(x) = p(x) + q(x), calculate p(10), q(10), s(10), p(10) + q(10).

 2

What polynomial added to x2 + 4x – 5 gives 2x2 – 3x + 1?