Question

Find a cubic polynomial with the sum sum of the product pf its zeros taken two at a time and the product of its zeros as 5, -2 and -24 respectively

Answer 1

Answer:

${x}^{3} - 5 {x}^{2} - 2x + 24$

Step-by-step explanation:

If α β γ are the zeroes of a cubic polynomial, the cubic polynomial is given by

${x}^{3} - ( \alpha + \beta + \gamma) {x}^{2} + ( \alpha \beta + \beta \gamma + \gamma \alpha )x - \alpha \beta \gamma$

Given

$\alpha + \beta + \gamma = 5$

$\alpha \beta + \beta \gamma + \gamma \alpha = - 2$

$\alpha \beta \gamma = - 24$

Calculation

Using these values in the above expression, we get

${x}^{3} - (5) {x}^{2} + ( - 2 )x - ( - 24)$

${x}^{3} - 5 {x}^{2} - 2x + 24$

is the required cubic polynomial.