Question

$if \: \alpha + \beta = 5 \: and \: { \alpha }^{3} + { \beta }^{3} = 35 \: find \: the \: quadradic \: equation \: whose \: roots \: are \: \alpha \: and \beta .$



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Answer 1

Answer:

x²-5x+6

Step-by-step explanation:

We know that,

a³+b³=(a+b)(a²+b²-ab)

Simplifying it further,

a³+b³=(a+b)((a+b)²-3ab)

Put the values,

7=25-3ab

ab=6

So, the quadratic equation is

x²-5x+6