Question

If x= -1/2 is a zero of the polynomial, p(x)= ax³ - x² + x + 4, find the value of 'a'

Answer 1

x=-1/2 p(x)=0
P(-1/2) = a(-1/2)^3 - (-1/2)^2 + (-1/2) + 4
0 = -1/8a + 1/4 -1/2 + 4. (LCM)
0= -1/8a + 15/4
-15/4 = -1/8a
-15/4 * 8/1 = a
-30 = a
Therefore the value of a is -30

Answer 2

x=-1/2

ax^3 -x^2 +x +4 =0
a[-1/2]^3 -[-1/2]^2 +[-1/2] +4 =0
-a/8 -1/4 -1/2 +4 =0
-a/8 +[-1-2+16]/4 =0
-a/8 +13/4 =0
-a/8 = -13/4
-a = [-13*8]/4
-a = -104/4
a= 26