How do you find the discriminant of 3x2+2x-7 and what does it tell you about the equation?
for 3x^2 + 2x - 7 = 0
discr = 4 -4(3)(-7) = +88
so you have real roots, both irrational
b^2-4ac
2^2 -4(3)(-7)
4 + 84 = 88 = 8*11
It tells you that there are two real roots because the discriminant is positive and that the roots will not be whole numbers because there will be a square root of 11 involved.
To find the discriminant of the quadratic equation 3x^2 + 2x - 7, we can use the formula:
Discriminant = b^2 - 4ac
The equation is in the form ax^2 + bx + c, where a = 3, b = 2, and c = -7.
Plugging these values into the formula, we have:
Discriminant = (2)^2 - 4(3)(-7)
= 4 + 84
= 88
The discriminant is 88.
The discriminant tells us about the nature of the roots of the quadratic equation.
If the discriminant is positive (greater than 0), then the equation has two distinct real roots.
If the discriminant is zero, the equation has one real root, which is a repeated root.
If the discriminant is negative (less than 0), then the equation has two complex conjugate roots.
In this case, the discriminant is positive (88), so the equation 3x^2 + 2x - 7 has two distinct real roots.
To find the discriminant of a quadratic equation in the form ax^2 + bx + c = 0, where a, b, and c are coefficients, you can use the formula:
Discriminant (D) = b^2 - 4ac
In the equation 3x^2 + 2x - 7, we have:
a = 3
b = 2
c = -7
Substituting the values into the formula, we get:
D = (2)^2 - 4(3)(-7)
= 4 + 84
= 88
The discriminant, D, in this case, is 88.
Now, what does this value tell us about the equation? The discriminant helps determine the nature of the quadratic equation's roots.
1. If D > 0 (positive), then the equation has two distinct real roots.
2. If D = 0, then the equation has one real root (also known as a repeated root).
3. If D < 0 (negative), then the equation has no real roots; it has two complex roots (conjugate pairs).
Since 88 is positive (D > 0), the equation 3x^2 + 2x - 7 has two distinct real roots.