Question

Find the cubic polynomial whose leading coefficient is 5 and zeroes are -1 ,1 and 2​

Answer 1

5x³ - 10x² - 5x + 10 is he cubic polynomial whose leading coefficient is 5 and zeroes are -1 ,1 and 2​

Cubic polynomial with zeros α, β and γ  is given by

k(x -α)(x - β)(x - γ) where k≠ 0

Substitute α = - 1, β= 1 and γ = 2 and k = 5 ( leading coefficient)

5(x -(-1))(x - 1)(x - 2)

= 5(x + 1)(x - 1)(x - 2)

= 5(x² - 1)(x - 2)

= 5(x³ - 2x² - x + 2)

= 5x³ - 10x² - 5x + 10

5x³ - 10x² - 5x + 10 is he cubic polynomial whose leading coefficient is 5 and zeroes are -1 ,1 and 2​

Answer 2

Concept Introduction: Cubic Polynomial Equations are very special equation.

Given:

We have been Given: Coefficient of Cubic Polynomial Equation is

$5$

The zeroes of the equation are

$- 1 \\ 1 \\ 2$

To Find:

We have to Find: Find the Cubic Polynomial Equation.

Solution:

According to the problem, Let

$k = 5 \\ \alpha = - 1 \\ \beta = 1 \\ \gamma = 2$

therefore putting in the formula,

$k(x - \alpha )(x - \beta )(x - \gamma )$

that gives,

$5(x + 1)( x - 1)(x - 2) \\ 5( {x}^{2} - 1)(x - 2) \\ 5( {x}^{2} (x - 2) - 1(x - 2)) \\ 5( {x}^{3} - 2 {x}^{2} - x + 2) \\ 5 {x}^{3} - 10 {x}^{2} - 5x + 10$

Final Answer: The Cubic Polynomial Equation is

$5 {x}^{3} - 10 {x}^{2} - 5x + 10$

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