Question

question:-

Form a quadratic polynomial whose zeroes are -4 and -7

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Answer 1

Answer:

Step-by-step explanation:

sum of zeroes = a + b =  - 4 - 7 = -11

product of zeroes = ab = - 4 x -7 =28

k[ x^2 -(a + b)x + ab]

x^2 + 11x + 28

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Answer 2

Answer :-

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

Explanation :-

Given

Zeroes of the polynomial are - 4 and - 7

Let

• α = - 4

• β = - 7

Finding the sum of zeroes and product of zeroes

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

Product of zeroes = αβ = - 4(-7) = 28

Finding the polyinomial whose zeroes are - 4 and - 7

Quadratic polynomial ax² + bx + c

= k{x² - x(α + β) + αβ}

[Where k ≠ 0]

= 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 are x² + 11x + 28.