Category: Algebra
"Published in Newark, California, USA"
Find the equation of a polynomial if the roots are 3, 1, and -√2.
Solution:
If
one of the root of the equation is given which is -√2 , then we need
to get its conjugate because we want to eliminate the radical sign
in the given equation. The conjugate of -√2 is √2 . Hence, the
equation or a factor from the product of a root and its conjugate is
Therefore, the equation of a polynomial is
Category: Algebra
"Published in Newark, California, USA"
Find the remaining roots of the equation
if 1 - i√2 is a root.
Solution:
If
one of the root of the equation is given which is 1 - i√2 , then we need
to get its conjugate because we want to eliminate the imaginary number and the radical sign
in the given equation. The conjugate of 1 - i√2 is 1 + i√2 . Hence, the
equation or a factor from the product of a root and its conjugate is
In order to get the other factor for the given equation, let's divide the given equation with the above equation, we have
Since there's no remainder in the division, then the other factor of the given equation is x² + 2x - 3.
Let's factor the other factor of the given equation as follows
If you equate each factor to zero, then the values of x are -3 and 1.
Therefore, the other roots of the given equation are -3 and 1.
Category: Algebra
"Published in Newark, California, USA"
Find the remaining roots of the equation
if 2 + √5 is a root.
Solution:
If
one of the root of the equation is given which is 2 + √5 , then we need
to get its conjugate because we want to eliminate the radical sign
in the given equation. The conjugate of 2 + √5 is 2 - √5. Hence, the
equation or a factor from the product of a root and its conjugate is
In order to get the other factor for the given equation, let's divide the given equation with the above equation, we have
Since there's no remainder in the division, then the other factor of the given equation is 2x + 3.
Therefore, the other root of the given equation is 
.
