Roots of Polynomials: Edexcel
Core Pure 1 Polynomial
Relationships ACTUAL EXAM
QUESTIONS WITH SOLVED
ANSWERS.
How do you express the sum of cubes of roots for a cubic equation? - CORRECT
ANSWER✅✅The sum of cubes is α³ + β³ + γ³ = (α + β + γ)³ - 3(α + β + γ)(αβ + βγ +
γα).
How do you express the sum of the squares of roots for a cubic equation? - CORRECT
ANSWER✅✅The sum of squares is α² + β² + γ² = (α + β + γ)² - 2(αβ + βγ + γα).
How do you find the new polynomial from roots transformed by a linear transformation?
- CORRECT ANSWER✅✅Use the transformation gα + h for roots α, β, γ, and δ.
How do you find the values of m and k in the equation mx² + 4x + 4m = 0? - CORRECT
ANSWER✅✅Set up the equations based on the relationships of the roots: α + β = -b/a
and αβ = c/a.
In the equation mx² + 4x + 4m = 0, what are the roots in terms of k? - CORRECT
ANSWER✅✅The roots are k and 2k.
What are the possible types of roots for a quadratic equation? - CORRECT
ANSWER✅✅A quadratic equation can have 2 real roots or 2 complex roots.
What is the equation for the roots of a polynomial after a linear transformation? -
CORRECT ANSWER✅✅The new polynomial can be expressed in terms of the original
polynomial's coefficients.
What is the formula for the product of the roots of a quartic polynomial? - CORRECT
ANSWER✅✅The product of the roots is αβγδ = e/a.
What is the formula for the sum of squares of roots for a quadratic equation? -
CORRECT ANSWER✅✅The sum of squares is α² + β² = (α + β)² - 2αβ.
What is the general form of a quadratic equation? - CORRECT ANSWER✅✅The
general form is ax² + bx + c = 0.
Core Pure 1 Polynomial
Relationships ACTUAL EXAM
QUESTIONS WITH SOLVED
ANSWERS.
How do you express the sum of cubes of roots for a cubic equation? - CORRECT
ANSWER✅✅The sum of cubes is α³ + β³ + γ³ = (α + β + γ)³ - 3(α + β + γ)(αβ + βγ +
γα).
How do you express the sum of the squares of roots for a cubic equation? - CORRECT
ANSWER✅✅The sum of squares is α² + β² + γ² = (α + β + γ)² - 2(αβ + βγ + γα).
How do you find the new polynomial from roots transformed by a linear transformation?
- CORRECT ANSWER✅✅Use the transformation gα + h for roots α, β, γ, and δ.
How do you find the values of m and k in the equation mx² + 4x + 4m = 0? - CORRECT
ANSWER✅✅Set up the equations based on the relationships of the roots: α + β = -b/a
and αβ = c/a.
In the equation mx² + 4x + 4m = 0, what are the roots in terms of k? - CORRECT
ANSWER✅✅The roots are k and 2k.
What are the possible types of roots for a quadratic equation? - CORRECT
ANSWER✅✅A quadratic equation can have 2 real roots or 2 complex roots.
What is the equation for the roots of a polynomial after a linear transformation? -
CORRECT ANSWER✅✅The new polynomial can be expressed in terms of the original
polynomial's coefficients.
What is the formula for the product of the roots of a quartic polynomial? - CORRECT
ANSWER✅✅The product of the roots is αβγδ = e/a.
What is the formula for the sum of squares of roots for a quadratic equation? -
CORRECT ANSWER✅✅The sum of squares is α² + β² = (α + β)² - 2αβ.
What is the general form of a quadratic equation? - CORRECT ANSWER✅✅The
general form is ax² + bx + c = 0.
