Question

If α and β are the roots of the polynomial f(x) = x2 + x + 1, then find α^2+β^2

Answer 1

$\underline\mathfrak{Question:}$

If α and β are the roots of the polynomial f(x) = x2 + x + 1, then find α^2+β^2

$\underline\mathfrak{Answer:}$

Given α and β are the roots of the polynomial f(x) = x2 + x + 1

→Sum of the roots

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

$\alpha + \beta = \frac{ - 1}{1} = - 1$

→Product of the roots

$\alpha \beta = \frac{c}{a}$

$\alpha \beta = \frac{1}{1} = 1$

→To know the required answer, let's square the sum of roots on both sides

${( \alpha + \beta ) }^{2} = {( - 1)}^{2}$

${ \alpha }^{2} + { \beta }^{2} + 2 \alpha \beta = 1$

${ \alpha }^{2} + { \beta }^{2} = 1 - 2$

${ \alpha }^{2} + { \beta }^{2} = - 1$

Have a good evening!

Answer 2

Answer:

f(x) = x2 + x + 1, then find α^2+β^2

Answer is -1