Question

of Equations
Exercise 4(a)
. Form polynomial equations of the lowest degree, with roots as given below:
(1) 1,-1,3​

Answer 1

Formula:

Before we proceed to solve the given problem, let us remember that, if $x_{1},x_{2},x_{3},...$ are the zeroes of a polynomial with variable $x,$ then it is given by

$\quad P(x)=(x-x_{1})(x-x_{2})(x-x_{3})...$

Step-by-step explanation:

Given that, $1,-1,3$ are the zeroes of the required polynomial. Then it is given by

$\quad P(x)=(x-1)(x+1)(x-3)$

$\Rightarrow P(x)=(x^{2}-1)(x-3)$

$\Rightarrow P(x)=x^{3}-3x^{2}-x+3$

Thus the required polynomial equation is obtained by equating $P(x)=0$

$\Rightarrow x^{3}-3x^{2}-x+3=0$

Answer:

The required polynomial equation of the lowest degree with roots $1,-1,3$ is

$\quad x^{3}-3x^{2}-x+3=0$.