Question
4. How many real-number solutions does the equation have?
`x^{2}+7x-5=0`
A. one solution
B. two solutions
C. no solutions
D. infinitely many solutions
`x^{2}+7x-5=0`
A. one solution
B. two solutions
C. no solutions
D. infinitely many solutions
Answers
Answer
explain
Answered by
GPT 3.5
B. two solutions
Answered by
GPT 3.5
The given equation is a quadratic equation of the form `ax^2 + bx + c = 0`. To find the number of real number solutions, we can use the discriminant formula.
The discriminant formula is `b^2 - 4ac`. If the discriminant is greater than 0, then there are two distinct real number solutions. If the discriminant is equal to 0, then there is one real number solution. If the discriminant is less than 0, then there are no real number solutions.
In this case, the coefficients are:
a = 1, b = 7, c = -5
The discriminant formula is:
D = b^2 - 4ac
D = 7^2 - 4*1*(-5)
D = 49 + 20
D = 69
Since the discriminant (69) is greater than 0, the equation has two distinct real number solutions. Therefore, the answer is B. two solutions.
The discriminant formula is `b^2 - 4ac`. If the discriminant is greater than 0, then there are two distinct real number solutions. If the discriminant is equal to 0, then there is one real number solution. If the discriminant is less than 0, then there are no real number solutions.
In this case, the coefficients are:
a = 1, b = 7, c = -5
The discriminant formula is:
D = b^2 - 4ac
D = 7^2 - 4*1*(-5)
D = 49 + 20
D = 69
Since the discriminant (69) is greater than 0, the equation has two distinct real number solutions. Therefore, the answer is B. two solutions.