Question

Write the quadratic equation whose roots are 1 and 2, and whose leading coefficient is 3.

Answer 1

Explanation:

Get the roots first

y = (x -1)(x - 2)

When y = 0, the two factors in turn can be equated to zero. That gives you the roots

x - 1 = 0 Add 1 to both sides

x = 1

x - 2 = 0 Add 2 to both sides

x = 2

Now you need to worry about the leading coefficient. Just put a 3 in front of the first factor.

y = 3(x - 1)(x - 2) Remove the brackets.

y = 3(x^2 - x - 2x + 2) Combine

y = 3(x^2 - 3x - 2) Remove the brackets.

Answer: y = 3x^2 - 9x - 6