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Discriminant Formula In Georgia
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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. If D = 0, then the equation has only one 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.
What is the value of the discriminant for the quadratic equation -3 = -x2 + 2x? Summary: The value of the discriminant for the quadratic equation -3 = -x2 + 2x is 16.
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.
Answer and Explanation: D = B 2 − 4 A C = ( − 10 ) 2 − 4 ( 3 ) ( 2 ) = 100 − 24 = 76 .
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.
Solution: As given, quadratic equation 3√3x2+10x+√3=0. Thus, discriminant of the given quadratic equation is 64.
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.
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.