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Discriminant Formula In Michigan
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When the discriminant is equal to 0, there is exactly one real root. When the discriminant is less than zero, there are no real roots, but there are exactly two distinct imaginary roots.
For the quadratic equation ax2 + bx + c = 0, the expression b2 – 4ac is called the discriminant. The value of the discriminant shows how many roots f(x) has: - If b2 – 4ac > 0 then the quadratic function has two distinct real roots. - If b2 – 4ac = 0 then the quadratic function has one repeated real root.
Components of the formula: The expression b 2 - 4 ac is called the discriminant of the formula. This term decides the number of real solutions for the given quadratic equation. Hence, it is called the discriminant.
To find the discriminant given the quadratic equation f(x)=ax^2+bx+c, simply record the values of a, b, and c and then substitute them into the discriminant formula: d=b^2-4ac. This will give the value of the discriminant. This also tells the number of roots and whether or not the roots are real or imaginary.
If the discriminant of a quadratic equation is 2, then the equation has One real solution .
The value of the discriminant shows how many roots f(x) has: - If b2 – 4ac > 0 then the quadratic function has two distinct real roots. - If b2 – 4ac = 0 then the quadratic function has one repeated real root. - If b2 – 4ac < 0 then the quadratic function has no real roots.
Solution: As given, quadratic equation 3√3x2+10x+√3=0. Thus, discriminant of the given quadratic equation is 64.
A root is nothing but the x-coordinate of the x-intercept of the quadratic function. The graph of a quadratic function in each of these 3 cases can be as follows. Important Notes on Discriminant: The discriminant of a quadratic equation ax2 + bx + c = 0 is Δ OR D = b2 − 4ac.
Steps for Finding the Discriminant of a Quadratic Equation Step 1: Identify the values of a, b, and c in the quadratic equation. Step 2: Substitute the values of a, b, and c into the quadratic formula. Step 3: Evaluate the discriminant, b 2 − 4 a c , which is the expression under the radical.
Example: Find the discriminant of the quadratic equation 2x2 - 3x + 8 = 0. Comparing the equation with ax2 + bx + c = 0, we get a = 2, b = -3, and c = 8. So the discriminant is, Δ OR D = b2 − 4ac = (-3)2 - 4(2)(8) = 9 - 64 = -55.