Question

would 3k^2 + 5k + 7 = 0 have no solutions? if so, why?

Answer 1

@Lily2913

Answer 2

k =(5-√-59)/6=(5-i√ 59 )/6= 0.8333-1.2802i

Answer 3

i don't understand

Answer 4

Raise k to the 2nd power

Answer 5

check the discriminant \(\huge\color{reD}{\rm b^2-4ac}\) `Discriminant`
you can use this to find if the equation is factorable or not
if ` b^2-4ac > 0` then there are 2 real zeros

if ` b^2-4ac = 0` then there is one real root
if ` b^2-4ac < 0` then you will get two complex roots (no -x-intercept)

Answer 6

((3 • k2) - 5k) + 7 = 0

Answer 7

Simplify 3k2-5k + 7
Trying to factor by splitting the middle term

2.1 Factoring 3k2-5k+7

The first term is, 3k2 its coefficient is 3 .
The middle term is, -5k its coefficient is -5 .
The last term, "the constant", is +7

Step-1 : Multiply the coefficient of the first term by the constant 3 • 7 = 21

Step-2 : Find two factors of 21 whose sum equals the coefficient of the middle term, which is -5 .

-21 + -1 = -22
-7 + -3 = -10
-3 + -7 = -10
-1 + -21 = -22
1 + 21 = 22
3 + 7 = 10
7 + 3 = 10
21 + 1 = 22

Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored

Equation at the end of step 2 :

3k2 - 5k + 7 = 0
Step 3 :

Solve 3k2-5k+7 = 0

Answer 8

if u got a quadratic equation of the form-\[ak^2+bk+c=0\]then the roots are given by-\[k=\frac{ -b \pm \sqrt{b^2-4\times a \times c} }{ 2a }\]

if the square root part is less than 0 i.e., it is negative will mean that the square root cannot be operated
and hence there are no real roots

try to calculate the square root part :)

Answer 9

so since i get 109 after finding b^2 - 4ac i got 109

Answer 10

no that's not correct
b^2 -4ac isn't equal to 109

Answer 11

-59?

Answer 12

yes :)

Answer 13

looks right so it's negative
b^2-4ac < 0 so no x-intercepts you will get complex roots

Answer 14

so since -59 is less than 0 it't not factorable?

Answer 15

right if the discriminant is less than 0 then no

Answer 16

unless you are able to use complex numbers, if not then no.

Answer 17

thx to all :)