Question

A quadratic polynomial whose zeroes are -3and 4 is ​

Answer 1

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.