Question

What are the solutions to the equation 3k² + k-3=0?

Approximate the value of both solutions. Round each answer to two decimal places. Enter your answers as

a list of numbers, separated with commas. Example: 3.25,4.16

k=

Answer 1

Explanation:

Solution

Solve with the quadratic formula

3k2+k−3=0 : k=(−1+√376)/6 , k=(−1−√376 )/6 (Decimal: k=0.84712…, k=−1.18046…)- Answer

Steps

3k2+k−3=0

Solve with the quadratic formula

For a quadratic equation of the form ax^2+bx+c=0,

the solutions are x1, 2=(−b±√b^2−4ac)/2a where a=3, b=1, c=−3

Substituting we have

k1, 2= [(−1±√1^2−4· 3(−3)]/2· 3

Apply rule 1^a=1 , therefore 1^2=1

=√1+4· 3· 3=√1+36

√1^2−4· 3(−3)=√37

Therefore,

k1, 2=(−1±√37)/2· 3

k1, 2=(−1±√37)/6

Separate the solutions

k1=(−1+√37)/6

k2=(−1−√37)/6

The solutions to the quadratic equation are:

k=(−1+√37)/6 , k=(−1−√37)/6

k1=0.84712 k2=−1.18046