Compute the value of the discriminant and give the number of real solutions to the quadratic equation.
2x^2+5x-7=0
Discrimnant=
number of real solutions=
The discriminant is b^2-4ac
I won't do all the work for you, but figure that number out.
-If its positive, theres two solutions
-If its negative there are no solutions
-If its zero theres one solution.
7x^2-2x+8=0
To compute the discriminant of a quadratic equation in the form of ax^2 + bx + c = 0, where a = 2, b = 5, and c = -7, you can use the formula:
Discriminant (D) = b^2 - 4ac.
In this case:
Discriminant (D) = (5)^2 - 4(2)(-7)
= 25 + 56
= 81.
So the value of the discriminant is 81.
To determine the number of real solutions of the quadratic equation, you need to consider the value of the discriminant.
If the discriminant is greater than zero (D > 0), the quadratic equation has two distinct real solutions.
If the discriminant is equal to zero (D = 0), the quadratic equation has one repeated real solution (or one real root).
If the discriminant is less than zero (D < 0), the quadratic equation has no real solutions (or no real roots).
In this case, the discriminant is 81, which is greater than zero (81 > 0). Therefore, the quadratic equation 2x^2 + 5x - 7 = 0 has two distinct real solutions.
To compute the value of the discriminant of a quadratic equation in the form of ax^2 + bx + c = 0, you can use the formula:
Discriminant = b^2 - 4ac.
For the given quadratic equation, 2x^2 + 5x - 7 = 0, a = 2, b = 5, and c = -7.
Substituting the values into the formula, we get:
Discriminant = (5)^2 - 4(2)(-7)
= 25 + 56
= 81.
Therefore, the value of the discriminant is 81.
To determine the number of real solutions, we need to consider the discriminant:
- If the discriminant is positive (greater than 0), then there are two distinct real solutions.
- If the discriminant is zero, then there is one real solution (a double root).
- If the discriminant is negative (less than 0), then there are no real solutions (two complex solutions).
In this case, the discriminant is 81, which is positive. Therefore, there are two distinct real solutions to the quadratic equation 2x^2 + 5x - 7 = 0.