Question

Find the zeroes of the polynomial p(x) = `x^2 + 4/3x − 4/3`.

Answer 1

We are given the quadratic polynomial:

`p(x) = x^2 + 4/3 x − 4/3`

Step 1: Using the Quadratic Formula

The quadratic formula is: `x = −b  ± sqrt (b^2 − 4ac)/(2a)`

For the given polynomial,
a =1,

b = `4/3`

c = `−4/3`

Step 2: Finding the Discriminant

`b^2 − 4ac = (4/3)^2 − 4(1)(−4/3)`

= `16/9 + 48/9 = 64/9`

= `sqrt (64/9) = 8/3`

Step 3: Computing the Roots

x = `(− 4/3 ± 8/3)/2`

x = `(− 4/3 ± 8/3)/2 = 4/6 = 2/3`

x = `(− 4/3 ± 8/3)/2 = −4/2 = −2`

`x = 2/3, x = −2`