Question

If a and ß are the zeroes of the quadratic polynomial f(x) = 3x² - 5x - 2, then a³ + ß³ is ​

Answer 1

Answer:

215/27

Step-by-step explanation:

$3x^{2} - 5x - 2$

$= 3x^{2} - 6x +x - 2\\\= 3x(x-2) + 1(x-2)\\ = (x-2)(3x+1)$

$x_{1} = 2 \\\\ x_{2} = -1/3$

as zeros are a and ß, so

$x_{1} = \alpha \\x_{2} =\beta$

so,

$\alpha ^{3} + \beta ^{3} = 8 + (-1/27)\\ 215/27$

Answer 2

Answer:

α³ + β³ is 215/27

Step-by-step explanation:

To find : Value of α³ + β³

Solution :

We have polynomial :

• f(x) = 3x² - 5x - 2

Finding zeros of polynomial :

$\implies$ 3x² - 5x - 2

$\implies$ 3x² - (6 - 1)x - 2

$\implies$ 3x² - 6x + x - 2

$\implies$ 3x(x - 2) + 1(x - 2)

$\implies$ (x - 2) (3x + 1)

Zeros :

• x - 2 = 0

$\implies$ x = 2

• 3x + 1 = 0

$\implies$ 3x = -1

$\implies$ x = -1/3

Zeros are 2 and -1/3.

• α = 2
• β= -1/3

Now,

We need to find α³ + β³ :

$\implies$ (2)³ + (-1/3)³

$\implies$ 8 + (-1/27)

$\implies$ 8 - 1/27

$\implies$ (216 - 1)/27

$\implies$ 215/27

Therefore,

Value of α³ + β³ is 215/27 .