SOLUTION: Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. 3, -13, and 5 + 4i

Algebra ->  Rational-functions -> SOLUTION: Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. 3, -13, and 5 + 4i      Log On


   



Question 1113596: Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.
3, -13, and 5 + 4i

Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
The zeros at 3 and -13 result in factors (x-3)(x+13)
The zero at 5+4i will be one of two zeros, where the 2nd zero is at 5-4i (complex roots come in conjugate pairs).
Assuming the form +x%5E2+%2B+bx+%2B+c+=+0+ and using the quadratic formula
+-%28b%2F2a%29+%2B-+sqrt%28%28b%5E2-4ac%29%29%2F%282a%29+
+++-b%2F%282a%29+=++5+ —> +b+=+-10+
+++sqrt%28%28b%5E2-4%2A1%2Ac%29%29%2F%282%2A1%29+=+4i+ —> +%28100-4c%29%2F4+=+-16+ —> +100-4c+=+-64+
—> +c+=+41+
+x%5E2+-+10x+%2B+41+ generates zeros at +5+%2B-+4i+
—
Putting it all together: +f%28x%29+=+%28x+-+3%29%28x+%2B+13%29%28x%5E2+-+10x+%2B+41%29+
…in expanded form: +highlight%28f%28x%29+=+x%5E4+-+98x%5E2+%2B+800x+-+1599%29+