Question

If $\alpha and \beta$ are the zeros of the quadratic polynomial $f(x)= ax^{2}+bx+c$,then evaluate
(i) $\alpha - \beta$
(ii) $\frac{1} {\alpha} - \frac {1}{\beta}$
(iii) $\frac{1} {\alpha}+ \frac {1}{\beta}-2\alpha \beta$
(iv) $\alpha^{2}\beta-\alpha\beta^{2}$

Answer 1

Given : α and β are the zeroes of the quadratic polynomial  f(x)= ax² + bx + c

Sum of the zeroes of the quadratic polynomial = −coefficient of x / coefficient of x²

α+β = −b/a …………………(1)

Product of the zeroes of the quadratic polynomial = constant term/ Coefficient of x²

αβ = c/a ……………………….(2)

SOLUTION OF (i) and (ii) IS IN THE ATTACHMENT  :

(iii) Given  :  1/α + 1/β - 2αβ

[1/α + 1/ β] - 2αβ

= [(α+β)/αβ]–2αβ  

=[ (- b/a) / c/a ] - 2 × c/a

[From eq 1 & 2]

= −b/a ×  a/ c - 2c/a

= - b/ c - 2c/a

= −[b/c + 2c/a]

Hence, the value of   1/α + 1/β - 2αβ is −[b/c + 2c/a]

(iv) Given : α²β + αβ²

α²β + αβ² = αβ(α+β)  

[By taking Common Factor αβ]

= c/a(−b/a)

[From eq 1 & 2]

= −bc/a²

Hence, the value of  α²β + αβ² is  −bc/a².

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

Step-by-step explanation:

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