Question

find a quadratic polynomial ,the sum and the product of its zeroes are -2 and -5 respectively

Answer 1

alpha+beta=-2
alphabeta=-5
x^2-(-2)X+(-5)
x^2+2x-5

Answer 2

Let alpha and beta are - 2 and - 5

A/ q

Sum of zeroes

$\alpha + \beta \\ \\ = > - 2 + ( - 5) \\ \\ = > - 2 - 5 \\ \\ = > - 7$

Product of zeroes

$\alpha \beta \\ \\ = > ( - 2)( - 5) \\ \\ = > 10$

Required polynomial

$k(x {}^{2} - ( \alpha + \beta )x + \alpha \beta ) \\ \\ = > k(x {}^{2} - ( - 7)x + 10) \\ \\ where \: k \: is \: constant \\ \\ = > x {}^{2} + 7x + 10$