Q26 of 109 Page 3

A quadratic polynomial, the sum of whose zeroes is 0 and one zero is 3, is

Given,

One of the polynomial is 3,

Sum of the zeros = 0

Now

Let the other zero be x,

x + 3 = 0

x = – 3

So,

Zeros of the polynomial are 3 and – 3

Product of the zeros = 3 × – 3 = – 9

Polynomial with zeros 3 and – 3 = x² – (0)x + ( – 9) = x² – 9

What should be added to the polynomial x² – 5x + 4, so that 3 is the zero of the resulting polynomial?

What should be subtracted to the polynomial x² – 16x + 30, so that 15 is the zero of the resulting polynomial?

If two zeroes of the polynomial x³ + x² – 9x – 9 are 3 and – 3, then its third zero is

If √5 and – √5 are two zeroes of the polynomial x³ + 3x² – 5x – 15, then its third zero is