If a polynomial has only two zeroes and they are 2 and 3, what is the polynomial?

x^{2} + 5 x + 6

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x^{2} - 5 x + 6

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x^{2} - 5 x - 6

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x^{2} - 4 x + 6

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Solution

The correct option is B $x^{2} - 5 x + 6$
Given, 2 and 3 are the zeroes
$\Rightarrow$ From factor theorem, we have $(x - 2)$ and $(x - 3)$ as the factors of the polynomial.

$∴$ the polynomial is $(x - 2) (x - 3)$

We know,
$(x + a) (x + b)$ = $x^{2} + (a + b) x + a b$

Comparing $(x + a) (x + b)$ with $(x - 2) (x - 3)$
We have,
$a = - 2$ and $b = - 3$

$∴$ The polynomial is
$x^{2} + (- 2 + (- 3)) x + (- 2) (- 3)$

$\Rightarrow$ $x^{2} - 5 x + 6$

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