Which value of b will cause the quadratic equation x2 + bx + 5 = 0 to have two real number solutions?
Mathematics · College · Tue Nov 03 2020
Answered on
Given the quadratic equation:
x^2 + bx + 5 = 0
determine the value of b to have two real number solutions.
Solution:
In order to identify the value of b, we must choose two numbers that when multiplied the product is 5. Since 5 is a prime number meaning its only factors are itself and 1, therefore we know that the solutions are 5 and 1. To determine the middle number, we must add 5 and 1 together, therefore the middle number is 6.
x^2 + bx + 5 = 0
x^2 + 6x + 5 = 0
Factoring the quadratic equation, we will have,
(x + 1)(x + 5) = 0
in order to get the values of x or the solutions, we equate each factor by 0
x + 1 = 0
x = -1
x + 5 = 0
x = -5
The two solutions are x = -1 and x = -5