BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015

15th Edition

ISBN: 9781608408405

Author: HOUGHTON MIFFLIN HARCOURT

Publisher: Cengage Learning

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Question

Chapter 3, Problem 7CT

To determine

To determine: The explanation to find the number and type of solutions of the quadratic equation. Also, use the discriminant to justify the answer.

Expert Solution & Answer

Answer to Problem 7CT

The discriminant of the quadratic equation is greater than zero and equation has two solutions.

Explanation of Solution

Given information:

The quadratic equation: −x2+12x+32=0

The graph of the equation:

BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015, Chapter 3, Problem 7CT

Formula used:

Discriminant formula:

The discriminant D of a quadratic equation ax2+bx+c=0 is,

D=b2−4ac

Discriminant conditions:

If D<0 ; then the roots of the quadratic equations are not real.

If D=0 ; then the roots of the quadratic equation are real and equal.

If D>0 ; then the roots of the quadratic equations are distinct real numbers.

Calculation:

The given quadratic equation is −x2+12x+32=0 .

It is seen in the graph that the curve of the quadratic equation intersects the x -axis at two points. This means the equation has two solutions.

Also, the discriminant of the quadratic equation is greater than zero.

To find the discriminant of the given equation, use the discriminant formula D=b2−4ac .

Substitute −1 for a , 12 for b and 32 for c in the above formula and simplify.

D=(12)2−24(−1)(32)=14+2(3)=14+6=254

It is seen that the discriminant is greater than zero.

So, the equation has two solutions.

Hence, the discriminant of the quadratic equation is greater than zero and equation has two solutions.

Chapter 3, Problem 6CT

Chapter 3, Problem 8CT

Chapter 3 Solutions

BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015

Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E Ch. 3.1 - Prob. 7E Ch. 3.1 - Prob. 8E Ch. 3.1 - Prob. 9E Ch. 3.1 - Prob. 10E

Ch. 3.1 - Prob. 11E Ch. 3.1 - Prob. 12E Ch. 3.1 - Prob. 13E Ch. 3.1 - Prob. 14E Ch. 3.1 - Prob. 15E Ch. 3.1 - Prob. 16E Ch. 3.1 - Prob. 17E Ch. 3.1 - Prob. 18E Ch. 3.1 - Prob. 19E Ch. 3.1 - Prob. 20E Ch. 3.1 - Prob. 21E Ch. 3.1 - Prob. 22E Ch. 3.1 - Prob. 23E Ch. 3.1 - Prob. 24E Ch. 3.1 - Prob. 25E Ch. 3.1 - Prob. 26E Ch. 3.1 - Prob. 27E Ch. 3.1 - Prob. 28E Ch. 3.1 - Prob. 29E Ch. 3.1 - Prob. 30E Ch. 3.1 - Prob. 31E Ch. 3.1 - Prob. 32E Ch. 3.1 - Prob. 33E Ch. 3.1 - Prob. 34E Ch. 3.1 - Prob. 35E Ch. 3.1 - Prob. 36E Ch. 3.1 - Prob. 37E Ch. 3.1 - Prob. 38E Ch. 3.1 - Prob. 39E Ch. 3.1 - Prob. 40E Ch. 3.1 - Prob. 41E Ch. 3.1 - Prob. 42E Ch. 3.1 - Prob. 43E Ch. 3.1 - Prob. 44E Ch. 3.1 - Prob. 45E Ch. 3.1 - Prob. 46E Ch. 3.1 - Prob. 47E Ch. 3.1 - Prob. 48E Ch. 3.1 - Prob. 49E Ch. 3.1 - Prob. 50E Ch. 3.1 - Prob. 51E Ch. 3.1 - Prob. 52E Ch. 3.1 - Prob. 53E Ch. 3.1 - Prob. 54E Ch. 3.1 - Prob. 55E Ch. 3.1 - Prob. 56E Ch. 3.1 - Prob. 57E Ch. 3.1 - Prob. 58E Ch. 3.1 - Prob. 59E Ch. 3.1 - Prob. 60E Ch. 3.1 - 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The explanation to find the number and type of solutions of the quadratic equation . Also, use the discriminant to justify the answer.

Videos

To determine: The explanation to find the number and type of solutions of the quadratic equation. Also, use the discriminant to justify the answer.

Answer to Problem 7CT

Explanation of Solution

Chapter 3 Solutions