Question

if alpha,beta,gama are roots of ax³+bx+c=0 then form equation having roots -2alpha,-2beta,-2gama​

Answer 1

Step-by-step explanation:

sorry don't know your answer

Answer 2

The value is \alpha^2+\beta^2+\gamma^2=\frac{b^2-2ac}{a^2}

Step-by-step explanation:

Given : If alpha beta gamma are the zeros of the polynomial f(x)=ax^3+bx^2+cx+d.

To find : The value of \alpha^2+\beta^2+\gamma^2 ?

Solution :

If \alpha,\beta,\gamma are the zeros of the polynomial ax^3+bx^2+cx+d.

Then,

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

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

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

Using identity,

\alpha^2+\beta^2+\gamma^2=(\alpha+\beta+\gamma)^2-2(\alpha \beta+\beta \gamma+\gamma\alpha)

\alpha^2+\beta^2+\gamma^2=(-\frac{b}{a})^2-2(\frac{c}{a})

\alpha^2+\beta^2+\gamma^2=\frac{b^2}{a^2}-\frac{2c}{a}

\alpha^2+\beta^2+\gamma^2=\frac{b^2-2ac}{a^2}

Therefore, the value is \alpha^2+\beta^2+\gamma^2=\frac{b^2-2ac}{a^2}