Question

7.If (x+a)(x+b)(x+c)=x³+14x²+59x+70, find the value of (i) a+b+c (ii)a²+b²+c²​

Answer 1

Answer:

(i) (a + b + c) = 14

(ii) a²+b²+c²​ = 78

Step-by-step explanation:

(x + a)(x + b)(x + c) =

(x^2 + bx + ax + ab)(x + c)

(x^3 + bx^2 + ax^2 + abx +cx^2 + bcx + acx + abc)

(x^3 +x^2(b + a + c ) + x(ab + bc + ca) + abc) = x³+14x²+59x+70

(i) (a + b + c) = 14

(ab + bc + ca) = 59

a²+b²+c²​ = (a + b + c )^2  - 2(ab + bc + ca)

a²+b²+c²​ = 14^2 - 118

(ii) a²+b²+c²​ = 78