Question

Quadratic equation. Find the value of m so that the roots of the equation (4 - m) x^2 + (2m + 4)x + (8m + 1) = 0 may be equal.

Answer 1

The quadratic has one root with multiplicity 2 if the discriminant is 0, which is

`(2m+4)^2-4(4-m)(8m+1)`

(That is, for a quadratic
`ax^2+bx+c`, the discriminant is
`b^2-4ac`.)

Set the discriminant equal to 0 and solve for
`m`:

`(2m+4)^2-4(4-m)(8m+1)=0`

`4m^2+16m+16+32m^2-124m-16=0`

`36m^2-108=0`

`36m(m-3)=0`

`\implies m=0\text{ or }m=3`