Question

if alpha , beta and gama be a zeros of polynomial p(x) such that (alpha +beta + gama) = 3 , ( alpha beta +beta gama+ gama alpha) = -10 and alpha beta gama = -24 then p(x) = ?
a) x^3 + 3x^2 - 10x +24
b) x^3 + 3x^2 +10x - 24
c) x^3 - 3x^2 -10x +24
d) none of these

Answer 1

option c will be the correct answer

Answer 2

we know that ,

→ Sum of zeroes = -b/a

$\alpha + \beta + \gamma = \frac{ - b}{a} \\ \\ 3 = \frac{ - b}{a}$

also,

→ product of zeroes= c/a


$\alpha \times \beta \times \gamma = \frac{c}{a} \\ \\ = - 24 = \frac{c}{a}$
and,

→ sum of products of zeroes= -d/a

$\alpha \beta + \beta \gamma + \alpha \gamma = - 10 = \frac{ - d}{a}$

→ now, comparing it with,


$a {x}^{3} + b {x}^{2} + cx + d$

we have,


a= -3 , and c= -24 , and d= 10


$a {x}^{3} - 3x^{2} - 24x + 10$

option d is correct: none of these.

___________________________