Question

find the quadratic polynomial with sum and product of its zero is 8 and 15 respectively
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Answer 1

Sum of zeros = - b/a

8 = - b/a

Product of zeros = c/a

15 = c/a

By comparing

a = 1, b = - 8 and c = 15

Therefore quadratic polynomial is

x² - 8x + 15

.

Hope it helps uh!

Keep calm and study hard

Thanks for asking

Answer 2

S O L U T I O N :

$\bf{\large{\underline{\bf{Given\::}}}}}$

The sum & product of It's zero is 8 and 15.

$\bf{\large{\underline{\bf{To\:find\::}}}}}$

The quadratic polynomial.

$\bf{\large{\underline{\bf{Explanation\::}}}}}$

Let α & β be the zeroes of the of the quadratic polynomial.

So;

$\underline{\mathcal{SUM\:OF\:THE\:ZEROES\::}}$

$\longrightarrow\sf{\alpha +\beta =\dfrac{-b}{a} =\dfrac{Coefficient\:of\:x}{Coefficient\:of\:x^{2} } }\\\\\\\longrightarrow\bf{\alpha +\beta =8}$

$\underline{\mathcal{PRODUCT\:OF\:THE\:ZEROES\::}}$

$\longrightarrow\sf{\alpha \times \beta =\dfrac{c}{a} =\dfrac{Constant\:term}{Coefficient\:of\:x^{2} } }\\\\\\\longrightarrow\bf{\alpha \times \beta =15}$

Now;

$\boxed{\bf{The\:required\:quadratic\:polynomial\::}}}}}$

$\longrightarrow\sf{x^{2} -(sum\:of\:zero)x+(product\:of\:zero)}\\\\\longrightarrow\sf{x^{2} -(8)x+15}\\\\\longrightarrow\bf{x^{2} -8x+15}$