Question

find a cubic polynomial with the sum, Sum of the product of its zeros taken two at a time and product of its zeros are 6, 3 and minus 10 respectively​

Answer 1

Answer:-

${x}^{3} - 6 {x}^{2} + 3x + 10$

Given:-

$\alpha + \beta + \gamma = 6$

$\alpha \beta + \beta \gamma + \gamma \alpha = 3$

$\alpha \beta \gamma = - 10$

To find :-

The required cubic polynomial.

Solution:-

We know that, a cubic polynomial is in the form of :-

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

Now, put the given value,

${x}^{3} - (6) {x}^{2} + (3)x - ( - 10)$

${x}^{3} - 6{x}^{2} + 3x + 10$

hence, the required cubic polynomial is :-

${x}^{3} - 6 {x}^{2} + 3x + 10$

Answer 2

Answer:

Step-by-step explanation: