Question

Find a cubic polynomial whose zeroes are a , b , y and a + B + y = 5 , ap + by + ya = -11 , aby = 3

Answer 1

Step-by-step explanation:

Given -

• α + β + γ = 5
• αβ + βγ + γα = -11
• αβγ = 3

To Find -

• A cubic polynomial

Now,

As we know that :-

• α + β + γ = -b/a

→ 5/1 = -b/a ..... (i)

And

• αβ + βγ + γα = c/a

→ -11/1 = c/a ..... (ii)

And

• αβγ = -d/a

→ 3/1 = -d/a ...... (iii)

Now,

From (i), (ii) and (iii) we get :-

a = 1

b = -5

c = -11

d = -3

As we know that :-

For a cubic polynomial :-

• ax³ + bx² + cx + d

→ (1)x³ + (-5)x² + (-11)x + (-3)

→ x³ - 5x² - 11x - 3

Hence,

The required cubic polynomial is x³ - 5x² - 11x - 3