Question

Write a quadratic equation with the given roots. Write the equation in the form of ax^2+bx+c=0 where a b and c are integers

Answer 1

You haven't provided the required roots, but I can tell you how to do this kind of exercises in general.

If the
`x^2` coefficient is 1, i.e. the equation is written like
`x^2+bx+c=0`, then you can say the following about the coefficients b and c:

• 
  `b` is the opposite of the sum of the roots
• 
  `c` is the multiplication of the roots.

So, for example, if we want an equation whose roots are 4 and -2, we have:

• 
  `4+(-2) = 4-2 = 2 \implies b = -2`
• 
  `4 \cdot (-2) = -8 \implies c = -8`

So, the equation is
`x^2-2x-8=0`

If your roots are rational, you can work like this: suppose you want an equation with roots 3/4 and 1/2. You have:

• 
  `(3)/(4)+(1)/(2) = (3)/(4)+(2)/(4) = (5)/(4) \implies b = -(5)/(4)`
• 
  `(3)/(4) \cdot (1)/(2) = (3)/(8) \implies c = (3)/(8)`

And so the equation is

`x^2 - (5)/(4) + (3)/(8) = 0`

In order to have integer coefficients, you can multiply both sides of the equation by 8:

`8x^2 - 10 + 3 = 0`