Question

find the discriminant and simplified radical roots of the following:
2x^2 + 11x + 5

Answer 1

Do you know discriminant formula?

Answer 2

\[ax^2 + bx + c\]

discriminant:
\[b^2 - 4ac\]

finding roots there are a few different ways
but since you have already found the discriminant:

\[x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}\]

Answer 3

if discriminant < 0 then there are no real roots , if discriminant is a perfect square then the equation factorises into (Ax+B)(Cx+D) form

Answer 4

so do i just keep it in the form of (-11 ±√81)/4

Answer 5

Discriminant: b^2 -4ac = 11^2 - 4 (2)(5) = 121 - 40 = 81.

x = (-11 ±√81 )/ 4 = ( -11 + 9) / 4 = -2/4 = -1/2
OR
x = ( -11 - 9) / 4 = -20/4 = -5.

Roots are: -1/2 and -5

Answer 6

@directrix okay so thats what i did before. i just thought since it said radical roots that i keep it in radical form.

so if i were given the equation x^2 - 63
the roots would be kept in radical for right?
x= ±3√7

Answer 7

Yes, those are in simplified radical form.

In the first problem, √ 81 was in radical form but not simplified radical form because
√ 81 = 9.

Answer 8

Minor Point: equation x^2 - 63-->
is not an equation but a quadratic expression.

x^2 - 63 = 0 is the equation to find the roots (x-intercepts) of the quadratic equation
y = x^2 - 63

Answer 9

so wait is my answer correct then ? x^2 - 63 = ±3√7

cause i'm asked to find the root of that as well

Answer 10

What is the equation you were given? I don't see it.

Answer 11

oh cause in the question it asks me to find the discriminant of 2x^2 + 11x +5
x^2-63,
and
5x^2-6x-2

Answer 12

x^2 - 63 = x^2 + 0x - 63 = 0.

discriminant: 0^2 - 4(1)(-63) = 0 + 252 = 252

What did you write for the discriminant of this?

Answer 13

yeah i got the same discriminant too

Answer 14

So, were you asked to find the roots also?

Answer 15

yep.
so what i did was after i put into the quadratic formula
i got (-0 ± √252)/2
= (± √36 x 7)/2
=(±6√7)/2
=±3√7

Answer 16

is that right?

Answer 17

Yes, but you lost the variable: x = ±3√7

This statement is incorrect
x^2 - 63 = ±3√7

The roots of x^2 - 63 = 0 are ±3√7 is correct.

Answer 18

so it must be written as: The roots of x^2 - 63 = 0 are ±3√7

Answer 19

Yes.
Did you get the discriminant and roots of 5x^2-6x-2 ?

Answer 20

yes i did. the discriminant is 76
and the roots of 5x^2-6x-2 =0 are - 6 ±2√9

Answer 21

@alexeis_nicole --> I got x = ( 3 ± √19 ) / 5 for
the roots of 5x^2-6x-2 =0. You check your work; I'll check mine.

Answer 22

okay this is what i got.
the discriminant is 76

the roots of 5x^2 - 6x -2
x= (6± √76)10
= (6± √4 x 19)10
= (6± 2√19)10

.. ? where did i go wrong ?

Answer 23

(6± 2√19) / 10
= 2 (3 ± √19 ) /10
= (3 ± √19 ) / 5 --> You didn't simplify the fractions.

Answer 24

OOOH ! okay. i forgot to simplify. thanks directix :)

Answer 25

You are welcome.