What is the height of a polynomial or an algebraic number?

Apr 2, 2012 ... ... b, and c. To calculate the roots of the equation the program calculates the discriminant D, given by D=b^2-4ac." Then it goes on to give me ... ... byĵ + bzk̂ Magnitudes: |a⃗|=√{ax2 +ay2+az2} |b⃗|=√{bx2 +by2+bz2} Scalar ... 4ac}}/{2a} Work (W), Mechanical Energy (E, Kinetic Energy (K)) ... Because the value of b2 – 4ac is less than zero, this equation will not have real solutions. Our answer will be 2x2 – 4x + 5 = 0. If we inspect all of the other ... The discriminant is B^2-4AC. Notice this is the portion of the formula inside the square root. If the discriminant = 0, then the formula degrades to x = -B ... Jun 4, 2014 ... 3 Answers 3 ... Δ=b2−4ac>0 means that the equation has two real solutions. Δ=b2−4ac<0 means that the equation has no real solutions, but two ... -b 소. / b2 - 4ac. 2a . Step 2: Write your answer in the appropriate form: 1. If b2 - 4ac > 0, then there are two real roots r1 and r2 and the general ... Recall from precalcu- lus algebra that if the discriminant b2 - 4ac is positive, the equation (2) has two distinct ... 2 ) + b(c1y0. 1 + c2y0. 2) + c(c1y1 + ... Jun 15, 2023 ... If the discriminant D < 0, then the quadratic equation ax 2 + bx + c = 0 will not have any real roots. b = 1/2 a. 29. + á

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what is b 2 4ac

• If we know the roots of a quadratic equation, can we find the discriminant without knowing the coefficients?
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• What is the relationship between the discriminant and the number of common roots of two polynomials?
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• What are the definitions of the focus and directrix?
• How does the discriminant behave under extensions of number fields?
• How does the discriminant help in finding the intervals where a quadratic expression is positive or negative?
• How can we use the discriminant to solve inequalities involving quadratic expressions?
• Why is the discriminant under the square root in the quadratic formula?
• We mentioned BCH codes earlier; are there other types of codes where discriminants are relevant?