AI tutor
Welcome to Bytelearn!
Letβs check out your problem:
Write a polynomial of least degree with real coefficients and with the root .
Full solution
Q. Write a polynomial of least degree with real coefficients and with the root .
- Recognize Property of Complex Roots: Recognize that if a polynomial has real coefficients and a complex root, then the complex conjugate of that root must also be a root of the polynomial. The complex conjugate of is .
- Write Root Factors: Write the factors associated with the roots and . The factors are and .
- Multiply Factors: Multiply the two factors to obtain the polynomial. We have: .
- Expand Using FOIL Method: Use the FOIL method to expand the product of the two binomials:.
- Simplify Expression: Simplify the expression by combining like terms and using the fact that : .
- Verify Standard Form: Verify that the polynomial is in standard form with a leading coefficient of : The polynomial is in standard form with a leading coefficient of .
