Form the quadratic equation whose roots are $2$ and $3$ .

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Solution

Let ' $m$ ' and ' $n$ ' be the roots $∴ m = 2, n = 3$
Sum of the roots $= m + n = 2 + 3 ∴ m + n = 5$
Product of the roots $= m n = (2) (3) ∴ m n = 6$
Standard form is $x^{2} - (m + n) x + m n = 0 ∴ x^{2} - (5) x + (6) = 0$
$∴ x^{2} - 5 x + 6 = 0$

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