Subject
গণিত
Topic
Algebra
Given roots 1 and −3 for a monic quadratic, find the polynomial.
Given roots 1 and −3 for a monic quadratic, find the polynomial.
ক)
x2− 2x − 3খ)
x2− 1x − 3গ)
x2+ 2x − 3ঘ)
x2− 4x + 3Explanation
Since the polynomial is monic and its roots are and , it factors as Expanding, Thus the correct choice is Option 3: .Related questions
Define the arithmetic mean (AM) of positive numbers x1, …, xn.For ax2+ bx + c = 0 with roots r1, r2, state Vieta’s relations.For ax3+ bx2+ cx + d with roots r1, r2, r3, state Vieta’s relations.From x2− 5x + 6 = 0, find the roots using Vieta.Real-coefficient polynomial with roots 2, 1 ± i; write the monic cubic.What are the elementary symmetric polynomials in roots r1,…,rn?Express r1^2 + r2^2 for a quadratic ax^2 + bx + c = 0 in terms of coefficients.For a cubic ax^3 + bx^2 + cx + d = 0, express Σ r_i^2 via coefficients.