Homework Help: Math 222
Posted by Tika on Monday, April 27, 2015 at 5:10pm.
Posted by Tika on Monday, April 27, 2015 at 1:08pm.
what is the value of the discriminant and of the real solutions of the quadratic equation?
5x^2-9x plus 2 equals 0
To find the value of the discriminant and the real solutions of a quadratic equation, you need to use the quadratic formula. The quadratic formula is:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this equation, a, b, and c are the coefficients of the quadratic equation in the form ax^2 + bx + c = 0.
For your equation, 5x^2 - 9x + 2 = 0, the coefficients are:
a = 5
b = -9
c = 2
To find the discriminant, you need to calculate b^2 - 4ac. So, in this case, it would be:
Discriminant = (-9)^2 - 4 * 5 * 2
Calculating this, we get the discriminant value:
Discriminant = 81 - 40 = 41
The value of the discriminant is 41.
To find the real solutions, you substitute the values of a, b, c, and the discriminant into the quadratic formula and solve for x. In this case, it would be:
x = (-(-9) ± √(41)) / (2 * 5)
Simplifying this equation, you get:
x = (9 ± √(41)) / 10
So, the real solutions of the quadratic equation 5x^2 - 9x + 2 = 0 are:
x = (9 + √(41)) / 10
x = (9 - √(41)) / 10
These are the two real solutions.