Question

solve the question
mathematics polynomials​

Answer 1

Answer:

(i) 7

(ii) ±$\sqrt{5}$

(iii) 3

Step-by-step explanation:

we know that,

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

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

∴α×β=1

⇒(α×β)²=1

∴α+β=3

⇒(α+β)²=9

⇒α²+β²+2×α×β=9

⇒α²+β²=7

⇒α²+β²-2αβ=7-2

⇒(β-α)²=5

⇒β-α=±√5

(i) $\frac{1}{\alpha ^{2} } +\frac{1}{\beta ^{2}}$ = $\frac{\alpha ^{2}+ \beta ^{2}}{\alpha ^{2} \beta ^{2}}$ = 7

(ii) $\frac{1}{\alpha} -\frac{1}{\beta }$ = $\frac{\beta - \alpha }{\alpha \beta }$ = ±$\sqrt{5}$

(iii) $\frac{1}{\alpha} +\frac{1}{\beta }$ = $\frac{\beta +\alpha }{\alpha \beta }$ = 3