Question

If -1 and 2 are two zeros of the polynomial 2x3-x2-5x-2. Then find its third zero

Answer 1

$x=\frac{-1}{2}$

Step-by-step explanation:

Let the third zeroes of the polynomial x

the two zeroes are given -1 and 2

so,

$(x+1)(x-2)=x^2-2x+x-2\\x^2-x-2$

by using remainder theorem

$\frac{2x^3-x^2-5x-2}{x^2-x-2}$

after dividing

$Quatient=2x+1=0\\ 2x=-1\\x=\frac{-1}{2}$

Answer 2

The third zero is $-\frac{1}{2}$

Step-by-step explanation:

• Given polynomial is $2x^3-x^2-5x-2$
• Also given that -1 and 2 are the zeros for the given polynomial
• Since the degree of the given polynomial is 3
• Therefore it has 3 zeros

To find the third zero :

By using Synthetic Division we can solve this polynomial

To find the zeros we have to equate the given polynomial to zero

$2x^3-x^2-5x-2=0$

-1 _|  2     -1      -5      -2

       0     -2       3       2

    _________________

      2      -3      -2       0

• Therefore x+1 is a factor
• Therefore x=-1 is a zero
• Now we have quadratic equation $2x^2-3x-2=0$

• $2x^2-4x+x-2=0$
• $2x(x-2)+1(x-2)=0$
• $(2x+1)(x-2)=0$
• 2x+1=0 or x-2=0
• $x=-\frac{1}{2}$ or x=2 are zeros

Since -1 and 2 are zeros (given)

Therefore the third zero is $-\frac{1}{2}$