Question

Find a quadratic expression with integer coefficients whose roots are rmula1" title="5/2+ 3i" alt="5/2+ 3i" align="absmiddle" class="latex-formula"> and $5/2-3i$.

Answer 1

Answer:

4x² -20x  +61

Step-by-step explanation:

the quadratic equation can be written as (x-root1)(x-root2)

(x-(5/2) -3i) (x-(5/2)+3i), distribute

x² -(5/2)x +3xi -(5/2)x + 25/4 -(15/2)i -3xi +(15/2)i -9i², simplify

x² -(5/2)x -(5/2)x + 25/4  -9i², use the fact that i² =(√-1)² = -1 and substitute i²

x² -(5/2)x -(5/2)x + 25/4 +9, combine like terms and rewrite 9 as 36/4

x² -(10/2)x  +25/4 + 36/4, combine like terms and simplify

x² -5x  +61/4 is the quadratic expression yet it does not have integer coefficients so multiply by 4 to have all coefficients integers

4x² -20x  +61