Question

For the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also find the zeroes of these polynomials by factorisation.

`(-8)/3, 4/3`

Answer 1

Sum of the zeroes = `- 8/3`

Product of the zeroes = `4/3`

P(x) = x² – (Sum of the zeroes) + (Product of the zeroes)

Then, P(x) = `x^2 - (-8x)/3 + 4/3`

P(x) = `3x^2 + 8x + 4`

Using splitting the middle term method,

3x² + 8x + 4 = 0

3x² + (6x + 2x) + 4 = 0

3x² + 6x + 2x + 4 = 0

3x(x + 2) + 2(x + 2) = 0

(x + 2)(3x + 2) = 0

`\implies` x = `-2, -2/3`