Step by step
The question
Question: write the quadratic equation with roots 0 and 7.
roots 0 and 7
1 Sum and product
The sum of the roots: 0 plus 7 is 7.
sum = 0 + 7 = 7
The product: 0 times 7 is 0.
product = 0 × 7 = 0
2 Write the equation
The equation with roots r and s is x minus r, times x minus s.
Opened up: x squared, minus the sum times x, plus the product.
x² − (sum)x + product = 0
(x − r)(x − s) = x² − (r + s)x + rs
Put the sum and the product in.
x² − 7x + 0 = 0
Careful!
The sum goes in with a minus in front: minus 7.
Careful: not x² + 7x = 0 ✗
Tidy the signs: x² − 7x = 0.
x² − 7x = 0
3 Check
Let's check: put each root in.
x = 0 gives 0.
x = 0: 0² − 7(0) = 0
And x = 7 gives 0 too.
So the equation is right!
x = 7: 7² − 7(7) = 0
Let's look back.
First: sum and product.
Then: write the equation.
Last: check.
Answer
x² − 7x = 0