Algebra 2 question

Question

Solve the equation and put it in a+bi form

f(X)=5x²+4x +1

Answer 1

Use the Quadratic Formula:

Answer 2

5x^2 +4x +1

x = -4/10 +/- .1sqr(16-20)

x = -.4+/-.2i

on the chance the problem really read 5x^2 +4x -1 then it factors

= (5x-1)(x+1) = 0

x = -1 or 1/5

Answer 3

Hello Lori,

For training purposes, I am going to show this using the completion of square method.

5x^2 + 4x + 1 original equation

Going to move the constant of one to the other side

5x^2 + 4x +. = -1

Divide through by leading coefficient

x^2 + (4/5)x +. = -1/5

take half of the X coefficient and square it and add it to both sides

x^2 + (4/5)x + 4/25 = -1/5 + 4/25

Now factor the left side and simplify the right side

(x+2/5)^2 = -1/25

now take the square root of both sides

sqrt((x + 2/5)^2 = sqrt(-1/25)

now simplify

x + 2/5 = +- sqrt(i^2)/5

Subtract subtract 2/5 from each side and simplify

x= -2/5 +- i/5

final answer is

(-2 + i)/5. And. (-2 - i)/5

you can substitute each of these into the original equation and see that they work

Answer 4

Use the quadratic formula for this polynomial.

x = -b + - √ (b² - 4 ac) all divided by 2a

where a = 5, b = 4 and c = 1.

So

x = -4 + - √ (4²- 4*5*1) all divided by 2*5

x = -4 + - √ (16 - 20) all divided by 10

x = -4 + - √ (-4) all divided by 10

x =(-4 + - 2i) / 10

x = -4/10 + - 2i/10

x = -2/5 + - i/5

x = -2/5 + - (1/5)i

This is (a + bi) form with a = -2/5 and b = + or - 1/5

To prove the answers are correct, substitute them one at a time into the original equation for x and see if you get an answer of 0.

5( -2/5 + (1/5)i)² + 4 (-2/5 + (1/5)i) +1 Substituting -2/5 + 1/5i into the equation for x.

5(4/25 + 2(-2/5)(1/5)i + 1/25 i² ) + (-8/5 + 4/5 i ) + 1 Foiling the binomial and multiplying

5( 4/25 - 4/25 i - 1/25) + (-8/5 + 4/5 I) + 1 Getting common denominators of 25

20/25 - 20/25 i - 5/25 - 40/25 + 20/25 i + 25/25 Collecting like terms

0

A similar check can be done for -2/5 - 1/5 i