Math

QuestionFind the discriminant of the equations: 83. x24x5=0x^{2}-4x-5=0 and 84. 4x22x+3=04x^{2}-2x+3=0. What does it reveal about solutions?

Studdy Solution

STEP 1

Assumptions1. The equations given are quadratic equations of the form ax+bx+c=0ax^ + bx + c =0. . The discriminant of a quadratic equation is given by =b4ac = b^ -4ac.
3. The discriminant indicates the number and type of solutions for the quadratic equation - If >0 >0, there are two distinct real solutions. - If =0 =0, there is one real solution. - If <0 <0, there are two complex solutions.

STEP 2

First, we need to identify the coefficients aa, bb, and cc in the quadratic equation x24x5=0x^{2}-4x-5=0.

STEP 3

In the equation x2x5=0x^{2}-x-5=0, the coefficients are a=1a=1, b=b=-, and c=5c=-5.

STEP 4

Now, we can calculate the discriminant $$ using the formula $ = b^2 -4ac$.

STEP 5

Substitute the values of aa, bb, and cc into the formula to calculate the discriminant for the first equation.
=(4)241(5) = (-4)^2 -4*1*(-5)

STEP 6

Calculate the discriminant for the first equation.
=16+20=36 =16 +20 =36

STEP 7

The discriminant of the equation x24x5=0x^{2}-4x-5=0 is 3636. Since >0 >0, there are two distinct real solutions.

STEP 8

Next, we need to identify the coefficients aa, bb, and cc in the quadratic equation 4x22x+3=04x^{2}-2x+3=0.

STEP 9

In the equation 4x22x+3=4x^{2}-2x+3=, the coefficients are a=4a=4, b=2b=-2, and c=3c=3.

STEP 10

Now, we can calculate the discriminant $$ using the formula $ = b^2 -4ac$.

STEP 11

Substitute the values of aa, bb, and cc into the formula to calculate the discriminant for the second equation.
=()443 = (-)^ -4*4*3

STEP 12

Calculate the discriminant for the second equation.
=448=44 =4 -48 = -44

STEP 13

The discriminant of the equation x22x+3=0x^{2}-2x+3=0 is 44-44. Since <0 <0, there are two complex solutions.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord