Verify that 3, -2, 1 are the zeros of the cubic polynomial $p (x) = x^{3} - 2 x^{2} - 5 x + 6$ and verify the relation betweeen its zeros and coefficients.

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Solution

p(x)= $p (x) = x^{3} - 2 x^{2} - 5 x + 6$

At x=3
P(3)= $(3)^{3} - 2 (3)^{2} - 5 (3) + 6$
=27-18-15+6
=0
since p(3)=0
hence 3 is a zero of p(x)

at x=-2
p(-2)= $(- 2)^{3} - 2 (- 2)^{2} - 5 (- 2) + 6$
=-8-8+10+6
=0
since p(-2)=0
hence -2 is a zero of p(x)

at x=1
p(1)= $(1)^{3} - 2 (1)^{2} - 5 (1) + 6$
=1-2-5+6
=0
Since p(1)=0
hence 1 is a zero of p(x)

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Verify that 3, -2, 1 are the zeros of the cubic polynomial p(x)=x3−2x2−5x+6 and verify the relation betweeen its zeros and coefficients.

p(x)=p(x)=x3−2x2−5x+6 At x=3 P(3)=(3)3−2(3)2−5(3)+6 =27-18-15+6 =0 since p(3)=0 hence 3 is a zero of p(x) at x=-2 p(-2)=(−2)3−2(−2)2−5(−2)+6 =-8-8+10+6 =0 since p(-2)=0 hence -2 is a zero of p(x) at x=1 p(1)= (1)3−2(1)2−5(1)+6 =1-2-5+6 =0 Since p(1)=0 hence 1 is a zero of p(x)

Verify that 3, -2, 1 are the zeros of the cubic polynomial $p (x) = x^{3} - 2 x^{2} - 5 x + 6$ and verify the relation betweeen its zeros and coefficients.