Question

Zeros of polynomial x cube minus 2 x square + 3 x minus 4 is equals to​

Answer 1

POLYNOMIAL AND ZEROS

Let $f(x)=ax^{3}+bx^{2}+cx+d$ be a polynomial of degree $3.$

If $\alpha,\beta,\gamma$ be its zeros, then the relation between zeros and coefficients states that:

$\quad\quad \alpha+\beta+\gamma=-\frac{b}{a}$

$\quad\quad \alpha\beta+\beta\gamma+\gamma\alpha=\frac{c}{a}$

$\quad\quad \alpha\beta\gamma=-\frac{d}{a}$

Step-by-step solution:-

The given polynomial is

$\quad\quad g(x)=x^{3}-2x^{2}+3x-4$

Comparing with the above polynomial $f(x)$, we get

$a=1,\:b=-2,\:c=3,\:d=-4$

Now the sum of the zeros of the polynomial is given by

$\quad\quad -\frac{b}{a}=-\frac{-2}{1}=\bold{2}$

Answer: The sum of the zeros is 2.

Answer 2

POLYNOMIAL AND ZEROS

Let $f(x)=ax^{3}+bx^{2}+cx+d$ be a polynomial of degree $3.$

If $\alpha,\beta,\gamma$ be its zeros, then the relation between zeros and coefficients states that:

$\quad\quad \alpha+\beta+\gamma=-\frac{b}{a}$

$\quad\quad \alpha\beta+\beta\gamma+\gamma\alpha=\frac{c}{a}$

$\quad\quad \alpha\beta\gamma=-\frac{d}{a}$

Step-by-step solution:-

The given polynomial is

$\quad\quad g(x)=x^{3}-2x^{2}+3x-4$

Comparing with the above polynomial $f(x)$, we get

$a=1,\:b=-2,\:c=3,\:d=-4$

Now the sum of the zeros of the polynomial is given by

$\quad\quad -\frac{b}{a}=-\frac{-2}{1}=\bold{2}$