Question

Verity that 1,2 and 3/2 are the zeror of the cubic
Polynomial p(x) = 2x^3-9x² +13x6. Then verify the relationship
between the zeros and the coefficients of the polynomial​

Answer 1

Step-by-step explanation:

$p(x) = 2x^3-9x² +13x - 6 \\ p(1) = 2(1)^3-9(1)² +13(1) - 6 \\ = 2 \times1 - 9 \times 1 + 13 - 6 \\ = 2 - 9 + 13 - 6 \\ = 0$

yes

$p(x) = 2x^3-9x² +13x - 6 \\ p(2) = 2(2)^3-9(2)² +13(2) - 6 \\ = 2 \times 8- 9 \times 4 + 26- 6 \\ = 16- 36+ 26 - 6 \\ = 0$

yes

$p(x) = 2x^3-9x² +13x - 6 \\ p( \frac{3}{2} ) = 2( \frac{3}{2} )^3-9( \frac{3}{2} )² +13( \frac{3}{2} ) - 6 \\ = 2 \times \frac{27}{8} - 9 \times \frac{9}{4} + \frac{39}{2} - 6 \\ = \frac{27}{4} - \frac{81}{4} + \frac{39}{2} - 6 \\ = \frac{27 - 81 + 78 - 24}{4} \\ = \frac{0}{4} \\ = 0$

yes