Question

21 Points

Solve the quadratic equation x2 − 4x + 10 = 0 using the quadratic formula. What is the solution when expressed in the form a ± bi, where a and b are real numbers?

Answer 1

Explanation:

The correct way to write that "x squared" is x^2. Thus, you have x^2 - 4x + 10 = 0.

This is a quadratic equation, with a = 1, b = -4 and c = 10. The discriminant, b^2-4ac, is thus (-4)^2-4(1)(10), or 16 - 40, or -26.

The two solutions are thus:

-(-4) plus or minus i√26

x = ------------------------------------

2(1)

or x = (4 + i√26)/2 and x = (4 - i√26)/2

Answer 2

What is the quadratic formula ?

... [- b ± √(b² - 4ac ) / 2a ]

Given :-

... x² - 4x + 10 = 0

Through this, we know ( a = 1 ) ( b = - 4 ) and ( c = 10 )

Plug in the values :-

... 4 ± √( 16 - 4(1)(10) ) / 2(1)

... 4 ± √( 16 - 40 ) / 2

... 4 ± √( -24 ) / 2

( Note :- 'i' is called √-1 )

... 4 ± √24/2 × √-1

... 4 ± (√24/2)i

If we represent this in the form of a±bi , we get ( a = 4 ) and ( b = √24/2)