Question

find a quadratic polynomial product and sum of whose zeroes are 2 and -1

Answer 1

Heya !

x
$x { }^{2} - sum \: ofthe \:zeroes \: (x) + produv \\ ct \: of \: the \: zeroes$
= x^2 - 2x +(-1)

=x^2 - 2x - 1 is the polynomial


Hope it helps you ^_^

Answer 2

Here's the formula,
$\alpha + \beta = \frac{ - b}{a} \\ \alpha \beta = \frac{c}{a}$
Sum of zeros = -b/a = 2/1
Product of zeros = c/a = -1/1

From here, we get
a = 1, b = -2, c = -1

ax^2 + bx + c = 0
${x}^{2} - 2x - 1 = 0$
This is the quadratic polynomial