Question

if alpha beta gamma are the zeros of the polynomial f(x)=ax3+bx2+cx+d, then alpha2+beta2+gamma2=

Answer 1

Answer:

Step-by-step explanation:

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

#Learn more

If alpha, beta, gamma are the zeroes of the polynomial f(x)=ax3+bx2+cx+d, then alphasquare+betasquare+gammasquare=

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