Question

find the quadratic polynomial whose zeroes are -3 and -5

Answer 1

The formula for making a quadratic equation is always x square-(alpha+Beta)x + (alpha*Beta)..
Here, alpha and beta are the zeroes of the polynomial.
So, the equation comes out to be
=x square-(-3+(-5))x + ((-3)*(-5))
= x square-(-8)x +15
=x square+8x+15 is the required quadratic equation.

Answer 2

$\alpha = - 3 \: \: \: \: \beta = - 5$
$\alpha + \beta = \frac{ - b}{a} = - 8 \\ \alpha \beta = \frac{c}{a} = 15$
from standard equation of polynomial
$a {x}^{2} + bx + c = 0 \\ {x}^{2} - \frac{ - b}{a} x + \frac{c}{a} = 0 \\ {x}^{2} - ( - 8)x + 15 = 0 \\ {x}^{2} + 8x + 15 = 0$
is the solution