Question

If ∝ and β are the roots of the quadratic equation x² – x – 2 = 0 then ∝² + β² is equal to​

Answer 1

Answer:

α² + β² = 5

Step-by-step explanation:

Given a quadratic equation in standard form

ax² + bx + c = 0 ( a≠ 0 ) , then

sum of roots = - $\frac{b}{a}$

product of roots = $\frac{c}{a}$

x² - x - 2 = 0 ← is in standard form

with a = 1, b = - 1, c = - 2 , then

α + β = - $\frac{-1}{1}$ = 1

αβ = $\frac{-2}{1}$ = - 2

Using the identity

(α + β)² = α² + β² + 2αβ , then

α² + β² = (α + β)² - 2αβ = 1² - 2(- 2) = 1 + 4 = 5

Answer 2

Answer :

$\large \boxed{ \boxed{\mathrm{ \alpha }^{2} + { \beta }^{2} = 5}}$

Given :

• $\alpha + \beta = 1$

• $\alpha \times \beta = - 2$

let's solve for :

• ${ \alpha }^{2} + { \beta }^{2}$

• ${ \alpha }^{2} + { \beta }^{2} + 2 \alpha \beta - 2 \alpha \beta$

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

let's plug the values,

• $(1) {}^{2} -2 \times ( - 2)$

• $1 + 4$

• $5$

$\mathfrak{best \: \: of \: \: luck \: \: for \: \: your \: \: assignment}$