Question

a quadratic polynomial , whose zeroes are -4 and -5 is​

Answer 1

$\overline{\underline{\boxed{\sf GIVEN \darr}}}$

a quadratic polynomial , whose zeroes are -4 and -5 is

$\overline{\underline{\boxed{\sf SOLUTION \darr}}}$

A quadratic polynomial in terms of the zeroes (α,β) is given by

x² - (sum of the zeroes)x + (product of the zeroes)

Given that zeroes of a quadratic polynomial are - 4 and - 5

• let α = - 4 and β= - 5

Therefore, substituting the value -4 and - 5 we get

• x² - (α + β)x + αβ

Putting the values we get

• x² - [ - 4 +(- 5)] x +(- 4)(- 5)

• x² + 9x + 20

Thus, x² + 9x + 20 is the quadratic polynomial whose zeroes are - 4 and -5.

Answer 2

Answer:

The quadratic equation is x² + 9x + 20 = 0

step-by-step explanation:

The only two possible answers for x are in the equations, which are second-degree equations in x. These two solutions for x are denoted as (α,β) and are also known as the roots of the quadratic equations. In the information that follows, we will study more about computed using the following roots. An algebraic equation of the second degree in x is a polynomial equation. The quadratic equation is written as ax2 + bx + c = 0,where x is the variables, a and b are the coefficients, and c is the positive constant.

Assume that α and β are the quadratic equation's roots.

Sum of the zeroes

$\alpha + \beta = -4-5$

$\alpha + \beta = -9$

the result of zeros

$\alpha \beta = 20$

Put these numbers in the place of in the basic quadratic equation.

$x^{2} - (\alpha + \beta )x + \alpha \beta = 0$

$x^{2} + 9x + 20 = 0$

The quadratic equation is 

$x^2 + 9x + 20 = 0$

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