Question

If the zeroes of the polynomial x^3- 3 x^2+x-1 are s/t , s and st then value of s is

Answer 1

Step-by-step explanation:

Ex 2.4, 3 If the zeroes of the polynomial x3 – 3x2 + x + 1 are a – b, a, a + b, find a ...

Answer 2

Answer: If the zeroes of the polynomial x^3- 3 x^2+x-1 are s/t, s, and st then the value of s is 1

Step-by-step explanation:

Definition of a polynomial:

a mathematical equation that contains one or more algebraic terms each of which includes a constant variable by one or more variables raised to a positive integral power.

Now here from the given question

The given polynomial equation is

p(x) = $x^3-3x^2+x-1$

therefore,

$\frac{s}{t} ,s, st$ are the given zeroes of the polynomial function p(x) = $x^3-3x^2+x-1$

Now here,

Let's add all the zeroes

That is,

Sum of its zeroes $\frac{s}{t} + s + st$ =$\frac{s + st + st^2}{t}$ = - $\frac{-3}{1\\}$ =  

$s + st + st^2 = 3t$                             .................(i)

$s + st^2 = (3 + s)t$                             .................(ii)

Now from the above equation,

Sum of the product of its zeroes :

$s(st) + s(\frac{s}{t}) + (st) (\frac{s}{t})$ = $s^2t + \frac{ s^2}{t} +s^2$ = $s^2(t + \frac{ 1}{t}+1)$ = $\frac{1}{1\\}$               .................(iii)

Now from the above equation,

from equation no. (i) and (iii),

It is coming to know that,

The value of s = 1.

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