Question

2 and 3 are the two zeros of polynomial x^3+5x^2-2x-24then find third zero​

Answer 1

Step-by-step explanation:

Given :

2 & 3 are the two zeros of the polynomial x³ + 5x² - 2x - 24.

To Find :

The 3rd zero of the polynomial,.

Solution :

The given polynomial contains mistake,.

It must be x³ - 5x² - 2x + 24,

Because,.

The given factor 3 is not true for the given equation,

p(x) =  x³ + 5x² - 2x - 24.

p(3) = (3)³ + 5(3)² - 2(3) - 24 = 27 + 45 - 6 - 24 = 42 ≠  0,.

(or) the given factor may be wrong,.

it can be  2 , -3 & -4 as follows,.

We know that,

Equation of the form,

ax³ + bx² + cx + d = 0, ( a ≠ 0),

Sum of the roots = $\frac{-b}{a}$

Products of the roots = $\frac{-d}{a}$

⇒ x³ + 5x² - 2x - 24

Here,

a = 1 , b = 5 , c = -2 , d = -24,.

Hence,

Sum of the roots = $\frac{-b}{a}$

⇒ 2 - 3 + y = $\frac{-5}{1}$

-1 + y = -5 ⇒ y = -4,.

(or)

Products of the roots = $\frac{-d}{a}$

⇒ 2 × (-3) × y = $\frac{-(-24)}{1}$

⇒ -6y = 24 ⇒ y = -4,.

If the polynomial is x³ + 5x² - 2x - 24 then , the third zero is -4,.

If the polynomial is x³ - 5x² - 2x + 24 then, the zeroes are , -2 , 3 , 4.