solve x^2-2x+10=0

Question

solve using the quadratic formula

Answer 1

The general formula for a quadratic equation is:

ax^2+bx+c=0

where a, b, and c are given, real numbers, usually integers. The quadratic formula is used to solve for x such that plugging the values found into the quadratic equation will result in the equation being equal to zero. The quadratic formula is:

 x = (-b ±√(b^2 – 4ac))/2a

Note that the ± symbol shows that there are two possible solutions. They could be real, the same (often referred to as repeated roots), or complex, depending on whether b²-4ac is positive, zero, or negative.

In this problem,

a=1

b=-2

c=10

The quadratic formula is then:

X=(-(-2)±√((-2)²-4(1*10))/2(1)

X=(2±√((4-40))/2

X=1±√(-36)/2

Because b²-4ac < 0, we know we have a complex number solution. Thus:

X=1±√(-36)/2

X=1±((√36)(√(-1)))/2

X=1±(6i)/2, where i refers to √(-1)

X=1±3i

This is the required solution.

You should verify the answer by plugging each of the two values