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Discriminant Formula In Riverside
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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.
Solution: As given, quadratic equation 3√3x2+10x+√3=0. Thus, discriminant of the given quadratic equation is 64.
In algebra, the discriminant, represented as uppercase delta (Δ), is a value calculated from the coefficients of a quadratic equation. It is used to determine the nature of the solutions to the equation. If Δ is greater than zero, the equation has two distinct real roots.
I.e., it discriminates the solutions of the equation (as equal and unequal; real and nonreal) and hence the name "discriminant". It is usually denoted by Δ or D. The value of the discriminant can be any real number (i.e., either positive, negative, or 0).
The discriminant is the part of the quadratic formula underneath the square root symbol: b²-4ac. The discriminant tells us whether there are two solutions, one solution, or no solutions.
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.
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.
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.
The discriminant (B2-4AC) is used to determine which conic section will result. If the discriminant is less than zero we have a circle (if A = C) or an ellipse; if the discriminant is equal to zero we have a parabola; if the discriminant is greater than zero we have a hyperbola.