Question

(i)If α,βare roots of ax^2+bx+c = 0,then αβ^2+α^2β+αβ is what 
(ii)if roots of a^2x^2-abx+c = 0 are consecutive integers then b^2-a^2 is
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Answer 1

$ax^2+bx+c=0\\\\If\ \alpha\ and\ \beta\ are\ roots,\ then\ \\\\(\alpha+\beta)=-\frac{b}{a},\ \ \ \alpha\beta=\frac{c}{a}\\\\\alpha\beta^2+\alpha^2\beta+\alpha\beta=(\alpha+\beta)\alpha\beta+\alpha\beta\\\\=-\frac{bc}{a^2}+\frac{c}{a}=\frac{(a-b)c}{a^2}$
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$a^2x^2-abx+c=0\\\\x_1+x_2=\frac{ab}{a^2}=\frac{b}{a},\ \ \ x_1x_2=\frac{c}{a^2}\\\\ (x_1-x_2)^2=\frac{b^2}{a^2}-4\frac{c}{a^2}=1,\ \ as\ |x_1-x_2|=1\\\\b^2-4c=a^2\\\\b^2-a^2=4c$

Answer 2

Answer:

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