Question

if 1 and -2 are two zeros of the polynomial x cube minus 4 x square - 7 x + 10 find its third zero​

Answer 1

Answer:

5

Step-by-step explanation:

Let the third zero be 'a'.

   As 1 , -2 and a are roots, (x - 1), (x + 2), (x - a) are factors of the given polynomials.

It means:

(x - 1)(x + 2)(x - a) = x³ - 4x² - 7x + 10

(x² + x - 2)(x - a) = x³ - 4x² - 7x + 10

x³ - ax² + x² - ax - 2x + 2a = x³ - 4x² - 7x + 10

x³ - x²(a - 1) - x(a + 2) + 2a = x³ - 4x² - 7x + 10

    Comparing values,

a - 1 = 4   ; a + 2 = 7   : 2a = 10

       Solving any of them:

   a - 1 = 4    ⇒ a = 5

Hence the third zero is 5

Answer 2

Step-by-step explanation:

to find the third zero of a cubic polynomial the formula is :- alpha + beta + gamma = -b/a

given:-

alpha = 1 &

beta = -2

to find gamma =

1 +(-2)+ gamma = -(-4)/1

1-2+ gamma= +4

-1 + gamma = 4

gamma= 4+1

= 5