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 22CR
To determine
To calculate: The discriminant of the
Expert Solution & Answer
Answer to Problem 22CR
The required discriminant of the equation is 16 and the equation has two real solutions.
Explanation of Solution
Given information:
The equation: x2+6x+5=0
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 equation is x2+6x+5=0 .
Rewrite the given equation as:
x2+6x+5=0
To find the discriminant of the above equation, use the discriminant formula D=b2−4ac .
Substitute 6 for b , 1 for a and 5 for c in the above formula.
D=(6)2−4(1)(5)=36−20=16
Since, the discriminant of the given equation is greater than 0;
So, the equation has two unequal and real solutions that is, the equation has two real solutions.
Hence, the required discriminant of the equation is 16 and the equation has two real solutions.
Chapter 3 Solutions
BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015
Ch. 3.1 - Prob. 1ECh. 3.1 - Prob. 2ECh. 3.1 - Prob. 3ECh. 3.1 - Prob. 4ECh. 3.1 - Prob. 5ECh. 3.1 - Prob. 6ECh. 3.1 - Prob. 7ECh. 3.1 - Prob. 8ECh. 3.1 - Prob. 9ECh. 3.1 - Prob. 10E
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