Question

If the sum of zeroes and product of zeroes of a quadratic polynomial are equal then what is the relation between their coefficients

Answer 1

Let the Quadratic Polynomial
$a {x}^{2} + bx + c$
have zeroes
$\alpha \: and \: \beta$

Sum of zeroes
$\alpha + \beta = \frac{ - b}{a}$
Product of Zeroes

$\alpha \beta = \frac{c}{a}$

If sum of zeroes equals product of zeroes, then,

$\alpha + \beta = \alpha \beta \\ \frac{ - b}{a} = \frac{c}{a } \\ \\ - b = c$