Equations and Inequalities – Relationship Between Roots and Coefficients of Cubic Equations (Basic)
Exams by Grade · K10 · Author: jaeinpark
Q1 When and are imaginary solutions of the quartic equation , find the value of . Q2 When are the solutions of the quartic equation , find the value of . Q3 For the solutions of the equation , the product of the real solutions is , and the product of the imaginary solutions is . Find the value of . Q4 When a cubic equation has solutions , and , find the value of . (Note, is a constant) Q5 When the cubic equation has a solution , find the value of . (Note, and are rational numbers) Q6 When the solutions of the cubic equation are and , find the value of . (Note, and are constants) Q7 Find the range of satisfying that the solutions of the cubic equation are all real. Q8 When the cubic equation has a real solution and two imaginary solutions, find the minimum value of the integer . Q9 Find the sum of all the feasible 's with which the cubic equation has a multiple root. Q10 Find the real number with which the cubic equation has two different real solutions. Q11 When and are the solutions of the cubic equation , find the value of . Q12 When the solutions of the cubic equation are and , find the value of . Q13 When and are the solutions of the cubic equation , find the value of . Q14 When and are the solutions of the cubic equation , it satisfies that . Find the value of constant . Q15 When the solutions of the cubic equation are and , find a cubic equation which has solutions and , and has a coefficient for the term . Q16 When the solutions of the cubic equation are and , find a cubic equation with 's coefficient and solutions and . Q17 For a cubic equation whose coefficient of is , it satisfies that . Find the value of in this case. Q18 When the cubic equation has a solution , find the value of for the rational numbers and . Q19 A cubic equation of which all the coefficients are real and the coefficient of is satisfies the following conditions: (A) is divisible by . (B) is a solution of the equation . Find the product of all the solutions of the equation . Q20 For a cubic equation of which all the coefficients are real and the 's coefficient is , find the value of when has two known solutions and .