Question
y=x²+12x+36
what is the number of solutions
what is the number of solutions
Answers
Answer
y=x²+14x+49
Answer
y=x²+3x-15
Answer
y=x²+x+13
Answer
y=x²+14x+50
Answer
y=x²-10x-23
Answered by
GPT 3.5
The given equation y = x² + 12x + 36 can be factored as (x + 6)².
Therefore, the number of solutions for this equation is 1, as the equation has only one root when a perfect square trinomial is factored.
Therefore, the number of solutions for this equation is 1, as the equation has only one root when a perfect square trinomial is factored.
Answered by
GPT 3.5
The given equation y = x² + 14x + 49 can be factored as (x + 7)².
Therefore, the number of solutions for this equation is 1, as the equation has only one root when a perfect square trinomial is factored.
Therefore, the number of solutions for this equation is 1, as the equation has only one root when a perfect square trinomial is factored.
Answered by
GPT 3.5
To determine the number of solutions for the given equation y = x² + 3x - 15, we can compute the discriminant (Δ) using the quadratic formula Δ = b² - 4ac, where the quadratic equation is in the form ax² + bx + c = 0.
In this case:
a = 1, b = 3, and c = -15
Δ = (3)² - 4*1*(-15)
Δ = 9 + 60
Δ = 69
Since the discriminant (Δ) is positive, there are two distinct real solutions for this quadratic equation.
In this case:
a = 1, b = 3, and c = -15
Δ = (3)² - 4*1*(-15)
Δ = 9 + 60
Δ = 69
Since the discriminant (Δ) is positive, there are two distinct real solutions for this quadratic equation.
Answered by
GPT 3.5
For the equation y = x² + x + 13, we can calculate the discriminant (Δ) using the quadratic formula, where the equation is in the form ax² + bx + c = 0.
In this case:
a = 1, b = 1, and c = 13
Δ = (1)² - 4*1*13
Δ = 1 - 52
Δ = -51
Since the discriminant (Δ) is negative, the quadratic equation has two complex conjugate solutions.
In this case:
a = 1, b = 1, and c = 13
Δ = (1)² - 4*1*13
Δ = 1 - 52
Δ = -51
Since the discriminant (Δ) is negative, the quadratic equation has two complex conjugate solutions.
Answered by
GPT 3.5
To determine the number of solutions for the given equation y = x² + 14x + 50, we need to calculate the discriminant (Δ) using the quadratic formula Δ = b² - 4ac, where the quadratic equation is in the form ax² + bx + c = 0.
In this case:
a = 1, b = 14, and c = 50
Δ = (14)² - 4*1*50
Δ = 196 - 200
Δ = -4
Since the discriminant (Δ) is negative, the quadratic equation does not have real solutions. The equation has two complex conjugate solutions that involve imaginary numbers.
In this case:
a = 1, b = 14, and c = 50
Δ = (14)² - 4*1*50
Δ = 196 - 200
Δ = -4
Since the discriminant (Δ) is negative, the quadratic equation does not have real solutions. The equation has two complex conjugate solutions that involve imaginary numbers.
Answered by
GPT 3.5
For the equation y = x² - 10x - 23, we can calculate the discriminant (Δ) using the quadratic formula, where the equation is in the form ax² + bx + c = 0.
In this case:
a = 1, b = -10, and c = -23
Δ = (-10)² - 4*1*(-23)
Δ = 100 + 92
Δ = 192
Since the discriminant (Δ) is positive, the quadratic equation has two distinct real solutions.
In this case:
a = 1, b = -10, and c = -23
Δ = (-10)² - 4*1*(-23)
Δ = 100 + 92
Δ = 192
Since the discriminant (Δ) is positive, the quadratic equation has two distinct real solutions.
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