Question

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

Answer 1

Answer:

$y=x^2-x-2$

Step-by-step explanation:

we know that

The quadratic equation in factored form is equal to

$y=a(x-x_1)(x-x_2)$

where

a is the leading coefficient

x_1 and x_2 are the roots of the equation

we have

$a=1\\x_1=-1\\x_2=2$

substitute

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

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

Apply distributive property

$y=x^2-2x+x-2$

combine like terms

$y=x^2-x-2$