Question

did a cubic polynomial whose zeros are 3 ,5 and -2​

Answer 1

Answer:

sum of zeroes = coefficient of x2coefficient of x3.

product of the zeroes = consent termcoefficient of x3.

sum of product of zeroes = coefficient of xcoefficient of x3.

sum of zeroes = coefficient of x2coefficient of x3.

product of the zeroes = consent termcoefficient of x3.

Answer 2

Answer:

Let the cubic polynomial be ax³ + bx² + cx + d

Given zeros →

$\alpha = 3$

$\beta = 5$

$\gamma = - 2$

Now,

$\alpha + \beta + \gamma = \frac{ - b}{a}$

$\implies \: 3 + 5 + ( - 2) = \frac{ - b}{a}$

$\implies \: 6 = \frac{ - b}{a}$

$\implies \: \frac{b}{a} = \frac{ - 6}{1}$

‡ b = -6 and. a = 1

$\alpha \beta + \beta \gamma + \gamma \alpha = \frac{c}{a}$

$\implies \: 3 \times 5 + 5 \times ( - 2) + ( - 2) \times 3 = \frac{c}{a}$

$\implies \: 15 - 10 - 6 = \frac{c}{a}$

$\implies \: 15 - 16 = \frac{c}{a}$

$\implies \: - 1 = \frac{c}{a}$

$\implies \: - 1 = \frac{c}{1}$

$\implies \bold{\: c \: = - 1}$

‡ c = -1

$\alpha \beta \gamma = \frac{ - d}{a}$

$\implies \: 3 \times 5 \times ( - 2) = \frac{ - d}{1}$

$\implies \: - 30 = - d$

$\implies \: \bold{d \: = 30}$

‡ d = 30

So, the cubic polynomial

→ x³ -6 x² - x + 1