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Discriminant Formula In Collin
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Collin
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US-000286
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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.
Reason: If discriminant (D) of a quadratic equation is less than zero, then the roots of the quadratic equation are imaginary.
The roots are calculated using the formula, x = (-b ± √ (b2 - 4ac) )/2a. Discriminant is, D = b2 - 4ac.
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.
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.
Solution: As given, quadratic equation 3√3x2+10x+√3=0. Thus, discriminant of the given quadratic equation is 64.
Use the discriminant formula to determine how many solutions. There are in this equation. So a isMoreUse the discriminant formula to determine how many solutions. There are in this equation. So a is one b is four and c is seven.
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.
The contribution of each discriminant function can be computed by λ i ∑ i = 1 s λ i which represents the relative importance of each discriminant function. Researchers should note that not always helpful results can be produced by discriminant analysis.