Question

let a , b and c be the roots of the equation x³ - 2x² + 4x + 10 = 0 then find the value of 1/2 ( a + 2 )(b + 2) (c + 2) . Actually it is 7 but I need the explanation .​

Answer 1

Ans: 7

step by step by explanation:

Given ,

a +b + c = -(-2)/1=2

ab + bc + ca. = 4

abc = - 10

1/2 (a +2)(b+2)(c+2)

= 1/2 (ab + 2a + 2b + 4)(c+2)

= 1/2 (abc +2ac +2bc + 4c +2ab +4a+4b+8)

=1/2( abc + 2(ab+bc+ca)+4(a+b+c)+8)

=1/2 ( -10 + 2(4) +4(2) +8)

=1/2 ( - 10 + 8+ 8+8) =1/2(24 -10)

=1/2 (14) = 7

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