Question

form a quadratic polynomial whose zeroes are -4 and -7.​

Answer 1

Answer :-

Polynomial whose zeroes are - 4 and - 7 is x² + 11x + 28.

Explanation :-

Given

Zeroes of the polynomial are - 4 and - 7

So

• α = - 4

• β = - 7

Sum of zeroes = α + β = - 4 + (-7) = - 4 - 7 = - 11

Product of zeroes = αβ = - 4(-7) = 28

Quadratic polynomial ax² + bx + c

= k{x² - x(α + β) + αβ}

[Where k ≠ 0]

By substituting the values

= k{x² - x(-11) + 28}

= k(x² + 11x + 28)

When k = 1

= 1(x² + 11x + 28)

= x² + 11x + 28

∴ the polynomial whose zeroes are - 4 and - 7 is x² + 11x + 28.

Answer 2

$\bf\large\underline{Answer:}$

x² + 11x + 28

$\bf\large\underline{Step-by-step explanation:}$

Given :-

Zeroes of polynomials are - 4 and - 7.

To find :-

We need to form a quadratic polynomial whose roots will be - 4 and - 7.

Solution :-

Let α and β be the roots of the quadratic polynomial in variable x.

Let α = - 4

Let β = - 7

•°• Sum of roots,α + β = (-4) + (-7)

α + β = - 4 - 7

α + β = - 11 ----> (1)

Product of roots, αβ = (-4) (-7)

αβ = 28 ----> (2)

Forming the quadratic polynomial,

=> x² - (α + β)x + (αβ)

Substitute the appropriate values of α+β and αβ,

=> x² - ( -11)x + (28)

=> x² + 11x + 28

•°• The quadratic polynomial whose zeroes are - 4 and - 7 is :

• x² + 11x + 28