Question

1
38. Find a cubic polynomial whose zeroes are 3, 1/2,- 1


​

Answer 1

Answer:

put in the formula

x^2 - sun of zeroes + x product of zeroes

Answer 2

Answer:

Let,

$\alpha = 3 \: \beta = 1 \div 2 \: and \: \gamma = - 1$

Then,

$( \alpha + \beta + \gamma ) = (3 + 1 \div 2 - 1) = 5 \div 2$

$( \alpha \beta + \beta \gamma + \gamma \alpha ) = (3 \div 2 - 1 \div 2 - 3) = - 4 \div 2 = - 2$

$and \: \alpha \beta \gamma = (3 \times 1 \div 2 \times ( - 1))= - 3 \div 2$

The polynomial with ZEROS α, β and γ is :

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

$= x {}^{3} - 5 \div 2 \: \: x {}^{2} - 2x + 3 \div 2$

Thus, 2x^3 - 5x^2 - 4x + 3 is the desired polynomial.

Step-by-step explanation:

@GENIUS