MATH SOLVE

2 months ago

Q:
# 8.Find the value of c that makes the expression be a perfect square trinomial p^2-30p+c9.Use quadratic formula to solve. 4x^2+7x-15=010.Find the number of real number solutions using the discrimination. x^2+4x-32=0Please help these are my final questions and I need help with them

Accepted Solution

A:

Hope this is the right one.

Problem 8

p^2 - 30p + c

Step One

Take 1/2 of - 30

1/2 * -30 = - 15

Step 2

Square -15

(-15)^2 = 225

c = 225

Problem Nine

[tex]\text{x = }\dfrac{ -b \pm \sqrt{b^{2} - 4ac } }{2a} [/tex]

a = 1

b = 4

c = -15

[tex]\text{x = }\dfrac{ -4 \pm \sqrt{4^{2} - 4*1*(-15) } }{2*1} [/tex]

[tex]\text{x = }\dfrac{ -4 \pm \sqrt{\text{16} + \text{60} } }{2} [/tex]

x = [-4 +/- sqrt(76)] / 2

x = [-4 +/- 2*sqrt19]/2

x = [-4/2 +/- 2/2 sqrt[19]

x = - 2 +/- sqrt(19)

x1 = - 2 + sqrt(19)

x2 = -2 - sqrt(19)

These two can be broken down more by finding the square root. I will leave them the way they are. It's just a calculator question if you want it to go into decimal form.

Problem Ten

a = 1

b = 4

c = -32

The discriminate is sqrt(b^2 - 4ac)

D = sqrt(b^2 - 4ac)

D = sqrt(4^2 - 4(1)(-32)

D = sqrt(16 - - 128)

D = sqrt(16 + 128)

D = sqrt(144)

D = +/- 12

Since D can equal + or minus 12 there must be 2 possible (and different) roots. As a matter of fact, this quadratic can be factored.

(x + 8)(x - 4) = y

But that' s not what you were asked for.

The discriminate is > 0 so the roots are going to be real.

Answer; The discriminate is > 0 so there will be 2 real different roots.

Problem 8

p^2 - 30p + c

Step One

Take 1/2 of - 30

1/2 * -30 = - 15

Step 2

Square -15

(-15)^2 = 225

c = 225

Problem Nine

[tex]\text{x = }\dfrac{ -b \pm \sqrt{b^{2} - 4ac } }{2a} [/tex]

a = 1

b = 4

c = -15

[tex]\text{x = }\dfrac{ -4 \pm \sqrt{4^{2} - 4*1*(-15) } }{2*1} [/tex]

[tex]\text{x = }\dfrac{ -4 \pm \sqrt{\text{16} + \text{60} } }{2} [/tex]

x = [-4 +/- sqrt(76)] / 2

x = [-4 +/- 2*sqrt19]/2

x = [-4/2 +/- 2/2 sqrt[19]

x = - 2 +/- sqrt(19)

x1 = - 2 + sqrt(19)

x2 = -2 - sqrt(19)

These two can be broken down more by finding the square root. I will leave them the way they are. It's just a calculator question if you want it to go into decimal form.

Problem Ten

a = 1

b = 4

c = -32

The discriminate is sqrt(b^2 - 4ac)

D = sqrt(b^2 - 4ac)

D = sqrt(4^2 - 4(1)(-32)

D = sqrt(16 - - 128)

D = sqrt(16 + 128)

D = sqrt(144)

D = +/- 12

Since D can equal + or minus 12 there must be 2 possible (and different) roots. As a matter of fact, this quadratic can be factored.

(x + 8)(x - 4) = y

But that' s not what you were asked for.

The discriminate is > 0 so the roots are going to be real.

Answer; The discriminate is > 0 so there will be 2 real different roots.