Question

product of zeros of the polynomial x cube minus 2 X square + 5 x + 6 is​

Answer 1

Answer:

Lets see:-

x cube+5x+6=0

(x+3)(x+2)=0

x+3=0

x=-3

x÷2=0

x=0

Hope it's help....

Answer 2

Product of zeros of the polynomial $x^{3}-2 x^{2}+5x+6$ is -6.

• The given polynomial is $x^{3}-2 x^{2}+5x+6$ . It is a cubic polynomial. Hence it has three roots.
• We have to find the product of roots. But manually calculating roots and then calculating the product is a cumbersome process. So we will use theory of equation to get the product of roots.
• According to theory of equation Any general polynomial of degree n ${\displaystyle P(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+\cdots +a_{1}x+a_{0}}$ if have complex roots $r_{1} ,r_{2},... , r_{n}$ then the product of roots, $\\r_{1}r_{2}\dots r_{n}=(-1)^{n}{\dfrac {a_{0}}{a_{n}}}.\end{cases}}}$
• So here n=3, $a_{n} = 1$ and $a_{0} = 6$
• So product of roots = $(-1)^{3}\frac{6}{1} = -6$