Question

find the polynomial whose zeros are 3 and -4​

Answer 1

ANSWER:

${x}^{2} + x - 12$

is a polynomial whose zeros are 3and-4

STEP-BY-STEP EXPLANATION

Answer 2

Answer :-

The polynomial whose zeroes are 3 and - 4 is x² + x - 12.

Solution :-

Given

Zeroes of a polynomial are 3 and - 4

So

• α = 3

• β = - 4

Now, find the sum of zeroes and product of zeroes

Sum of zeroes = α + β

= 3 + (-4)

= 3 - 4

= - 1

Product of zeroes = αβ

= 3(-4)

= - 12

Quadratic polynomial ax² + bx + c = k[x² - x(α + β) + αβ]

(Where k ≠ 0)

Here

• α + β = - 1

• αβ = - 12

By substituting the values

= k[x² - x(-1) + (-12)]

= k(x² + x - 12)

When k = 1

= 1(x² + x - 12)

= x² + x - 12

Therefore the polynomial whose zeroes are 3 and - 4 is x² + x - 12.