Question

If one root of x²+bx+c is double the other. Show 2b²=9ac

Answer 1

let one root be "alpha" another will be 2(alpha) . use sum of roots i.e. 3alpha= –b and product of roots i.e. 2alpha²=c . now eliminate alpha by squaring first eqⁿ. u will get 2b²=9ac
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Answer 2

one root=alpha
another root=2alpha
alpha+2alpha= -b/1
alpha= -b/3

(alpha)(2alpha)=c/1
2alpha^2=c
2(-b/3)^2=c
2b^2/9=c
2b^2=9c




note; you didnt used a in identity so a will not come in ans also



thanks
maths student