If z1, z2 are roots of z^2 - z + 2 = 0, what is z1 z2?

Boost your skills in A Level Further Mathematics Core Pure. Study with flashcards and multiple choice questions, each question is followed by hints and explanations. Get prepared for your exam with confidence!

Multiple Choice

If z1, z2 are roots of z^2 - z + 2 = 0, what is z1 z2?

For a quadratic with leading coefficient 1, the product of the roots equals the constant term. Writing the quadratic as (z − z1)(z − z2) expands to z^2 − (z1 + z2)z + z1 z2. Comparing with z^2 − z + 2 gives z1 + z2 = 1 and z1 z2 = 2. So the product z1 z2 is 2. As a quick check, the roots are (1 ± i√7)/2, and their product is [(1 + i√7)/2]·[(1 − i√7)/2] = (1 + 7)/4 = 2.

For a quadratic with leading coefficient 1, the product of the roots equals the constant term. Writing the quadratic as (z − z1)(z − z2) expands to z^2 − (z1 + z2)z + z1 z2. Comparing with z^2 − z + 2 gives z1 + z2 = 1 and z1 z2 = 2. So the product z1 z2 is 2. As a quick check, the roots are (1 ± i√7)/2, and their product is [(1 + i√7)/2]·[(1 − i√7)/2] = (1 + 7)/4 = 2.

More practice questions