Question

Find the quadratic equation given that the roots are 3 and 9
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Answer 1

`\bold\purple{Quadratic \: \: eq {}^(n) = x {}^(2) - ( \alpha + \beta )x + \alpha \beta} \\`

Sum of roots ,

`( \alpha + \beta ) = (3 + 9) = 12`

Product of roots ,

`( \alpha \beta ) = (3)(9) = 27`

Substituting the values in the above equation ,

`\bold{x {}^(2) - ( \alpha + \beta )x + \alpha \beta} \\\\ \bold{⇢ x {}^(2) - (12)x + 27} \\\\ \bold\blue{ ⇢x {}^(2) - 12x + 27}`

hope helpful~