Question

Name: A. Directions: Choose the letter of your answer for each question and write it on the space before each number a. a. a. a. a. 1. This is the value of the expression b2 - 4ac in the quadratic formula. b. discriminant C. extraneous root nature of roots d. solutions 2. If b2 - 4ac = 0, what is the nature of the roots? real, rational, equal c. real, irrational, unequal b. real, rational, unequal d. imaginary 3. What is the discriminant of the quadratic equation x2 + x - 56 = 0? - 225 b. 25 c. 225 d. -223 4. If the roots of a quadratic equation are - 7
= 0 c. x2 - 16X - 63 = 0 b. x2 + 2x - 63 = 0 d. x2 - 2x + 63 = 0 8. If b2 - 4ac ​

Answer 1

Step-by-step explanation:

jduxhlxieujcysoydgizoy

Answer 2

Answer:

1. b)Discriminant

2. a) real, rational, equal

3. c)225

4. d)x2 - 2x + 63 = 0

Step-by-step explanation:

1. Discriminant

b²-4ac is called a discriminant which is to find the number of roots in the equation.

2.b²-4ac=0

       b²-4ac>0 ==> 2 solution

       b²-4ac=0 x=-b/2a

       b²-4ac<0=no real solutions

      a)Real, rational, equal

3. x² + x - 56 = 0

  a=1

  b=1

  c=-56

-b±$\sqrt{b^{2}-4ac }$ /2a

-1±$\sqrt{1^{2}-4(1)(-56) }$/2(1)

-1±$\sqrt{1^{2}-4(1)(-56) }$/2

-1±$\sqrt{1-4(-56) }$/2

-1±$\sqrt{1+224) }$/2

-1±$\sqrt{225}$/2  ===>

-1±15/2

(-1+15)/2 ,(-1-15)/2

14/2,-16/2

7,-8

x+7=0 x=-7

x-8=0  x=8

These are the roots

$\sqrt{b^{2}-4ac }$ =-$\sqrt{1-4(-56) }$=$\sqrt{1+224) }$=$\sqrt{225}$

C)225

4.d. x2 - 2x + 63 = 0

Product=63

Sum=-2

7×(-9)=63

7-9=-2

x² +7x-9x - 63=0

x(x+7)-9(x+7)=0

(x-9)(x+7)=0

x=9

x=-7