Question

help?

Answer 1

Find the value of the discriminant for each quadratic equation below. Show all steps needed to write the answer in simplest form, including substituting the values of a, b, and c in the discriminant formula. Then use the value to determine how many real number solutions each equation has.

5x^2 + x = 4

Answer 2

HI!!

Answer 3

Hey :)

Answer 4

start by setting it equal to zero go from \[5x^2 + x = 4\] to
\[5x^2+x-4=0\]

Answer 5

\[\large \color{red}ax^2+\color{blue}bx+\color{green}c=0\]
\[\huge \color{red}5x^2+\color{blue}1x+\color{green}{-4}=0\]

Answer 6

then as @risn said compute
\[\huge \color{blue}b^2-4\times \color{red}a\times \color{green}c\]

Answer 7

D= 1 - 4 (1)(-4)?

Answer 8

nope

Answer 9

\(\color{red}a=\color{red}{5}\)

Answer 10

oh sorry.

D = 1-4(5)(-4)

Answer 11

yeah that is right
what do you get?

Answer 12

81?

Answer 13

as my final answer?

Answer 14

yeah me too

Answer 15

at the end of the question it asks us "Then use the value to determine how many real number solutions each equation has".

Answer 16

that is the answer to
Show all steps needed to write the answer in simplest form, including substituting the values of a, b, and c in the discriminant formula.

Answer 17

ok two steps here
81 is positive, so there are two real solutions
also 81 is a "perfect square" it is the square of 9
that means both solutions are rational numbers

Answer 18

oh ok! thank u so much! :)

Answer 19

in fact that means \[5x^2+x-4=0\] can be solved by factoring
you get
\[(5x-4)(x+1)=0\] so
\[x=\frac{4}{5}\] or \[x=-1\]

Answer 20

\[\color\magenta\heartsuit\]