Question

If a and b are the roots of the equation 6x²-22x-15=0 calculate the value of a-b

Answer 1

`(√(211))/(3)\approx4.842`

Explanation:

given a quadratic equation
`ax^2+bx+c=0`, we can find the roots through the quadratic formula.

we have roots
`x=(-b\pm√(b^2-4ac))/(2a)` and now if we subtract one root from the other we have:

`(-b+√(b^2-4ac))/(2a)-(-b-√(b^2-4ac))/(2a)=(2√(b^2-4ac))/(2a)=(√(b^2-4ac))/(a)` as the difference of roots.

now, we substitute values from the given equation
`6x^2-22x-15=0`.

the discriminant here is
`(-22)^2-4(-15)(6)=484+360=844=4* 211`

then, we have
`(√(4*211))/(6)=(2√(211))/(6)=(√(211))/(3)`. that is the difference of roots.