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Discriminant Formula In North Carolina
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Reason: If discriminant (D) of a quadratic equation is less than zero, then the roots of the quadratic equation are imaginary.
Solution: As given, quadratic equation 3√3x2+10x+√3=0. Thus, discriminant of the given quadratic equation is 64.
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.
The discriminant formula is used to determine the nature of the roots of a quadratic equation. The discriminant of a quadratic equation ax2 + bx + c = 0 is D = b2 - 4ac. If D > 0, then the equation has two real distinct 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.
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.
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.
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.
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).