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Discriminant Formula In Kings
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Discriminant of a Polynomial The discriminant of a quadratic polynomial is the portion of the quadratic formula under the square root symbol: b2-4ac, that tells whether there are two solutions, one solution, or no solutions to the given equation.
The given equation is of the form ax2 + bx + c = 0 where a = 2 b = – 4 andc = 3. Therefore the discriminantb2 – 4ac = – 42 – 4 × 2 × 3 = 16 – 24 = – 8 < 0So the given equation has no real roots.
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.
Delta Symbol: Discriminant This polynomial equation is almost always the quadratic equation. Consider the quadratic ax2+bx=c, the discriminant of this equation would equal b2-4ac, and it would certainly look like this: Δ= b2-4ac.
Solution: As given, quadratic equation 3√3x2+10x+√3=0. Thus, discriminant of the given quadratic equation is 64.
The discriminant of a quadratic equation ax2 + bx + c = 0 is in terms of its coefficients a, b, and c. i.e., Δ OR D = b2 − 4ac.
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.
If the discriminant is greater than zero, this means that the quadratic equation has two real, distinct (different) roots. x2 - 5x + 2. If the discriminant is greater than zero, this means that the quadratic equation has no real roots.
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.
If the discriminant is greater than zero, this means that the quadratic equation has two real, distinct (different) roots.