Question

Find the Polynomial whose
zeroes are 5 and 12​

Answer 1

Here, two zeroes of a polynomial are 5 and 12 respectively.

• We've to find the quadratic polynomial.

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As we know that, formula for finding a quadratic polynomial is :

$\:$

$\underline{\boxed{\sf\pink{quadratic \: polynomial =x {}^{2} - (sum \: of \: zeroes)x + product \: of \: zeroes}}}$

$\: \:$

$\bigstar \: \underline \mathfrak{substituting \: the \: values \: : }$

$\: \:$

$\sf :\implies \: quadratic \: polynomial \: = x {}^{2} - (sum \: of \: zeroes)x + product \: of \: zeroes \\ \\ \\ \sf :\implies \: quadratic \: polynomial = x {}^{2} - (5 + 12)x +( 5 \times 12) \\ \\ \\ \sf :\implies \: \underline{\boxed{\mathfrak\purple{quadratic \: polynomial = x {}^{2} - 17x + 60}}} \: \bigstar$

$\: \:$

$\sf\therefore{\underline{Hence, \: the \: quadratic \: polynomial \: is \: \bold{x {}^{2} - 17x + 60}.}}$