5. If the zeroes of the polynomial x3-3x2 + x + 1 are in A.P (i.e., a-

1.	5. If the zeroes of the polynomial x3-3x2 + x + 1 are in A.P (i.e., a-d, a and a + d) then find thenature of a +d
Answer» X³-3x²+x+1The zeroes of the polynomial are (a+d),a, (a-bd) Let α=a-dβ=aγ=a+d α+β+γ=-x² coefficient/x³ coefficient a-d+a+a+d=-3/13a=-3a=-3/3a= -1 αβγ= -constant/x³ coefficient (a-d)(a)(a+d)=-1/1(a²-d²)(a)= -1[(-1)²-d²](-1)=-1(1-d²)= -1/-11-d²=11-1=d²d²=0d=√0=0Therefore, a=-1 and d=0 Like my answer if you find it useful!

5. If the zeroes of the polynomial x3-3x2 + x + 1 are in A.P (i.e., a-d, a and a + d) then find thenature of a +d

Answer»

X³-3x²+x+1The zeroes of the polynomial are (a+d),a, (a-bd) Let α=a-dβ=aγ=a+d

α+β+γ=-x² coefficient/x³ coefficient a-d+a+a+d=-3/13a=-3a=-3/3a= -1

αβγ= -constant/x³ coefficient (a-d)(a)(a+d)=-1/1(a²-d²)(a)= -1[(-1)²-d²](-1)=-1(1-d²)= -1/-11-d²=11-1=d²d²=0d=√0=0Therefore, a=-1 and d=0

Like my answer if you find it useful!