Find a quadratic polynomial, the sum and product of whose zeroes are -

1.	Find a quadratic polynomial, the sum and product of whose zeroes are -8/3 and 4/3, respectively. Also find its zeroes.
Answer» 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)= x² – 8x/3 + 4/3 P(x)= 3x² – 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 ⇒ x = 2, 2/3

Find a quadratic polynomial, the sum and product of whose zeroes are -8/3 and 4/3, respectively. Also find its zeroes.

Answer»

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)= x² – 8x/3 + 4/3

P(x)= 3x² – 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

⇒ x = 2, 2/3