If alpha and beta are the roots of the equation x^2-4x+1=0, what is the value of alpha^2+beta^2?
Answer and explanation
Correct answer: 14
By Vieta’s formulas, alpha+beta=4 and alpha beta=1. Therefore, alpha^2+beta^2=(alpha+beta)^2-2alpha beta=4^2-2(1)=14. Hence, the correct answer is 14. Choosing 16 results from using only (alpha+beta)^2 and missing the term -2alpha beta. Exam tip: For the sum of the squares of roots, use alpha^2+beta^2=(alpha+beta)^2-2alpha beta.
Frequently asked questions
What is the correct answer to this question?
14
Why is this the correct answer?
By Vieta’s formulas, alpha+beta=4 and alpha beta=1. Therefore, alpha^2+beta^2=(alpha+beta)^2-2alpha beta=4^2-2(1)=14. Hence, the correct answer is 14. Choosing 16 results from using only (alpha+beta)^2 and missing the term -2alpha beta. Exam tip: For the sum of the squares of roots, use alpha^2+beta^2=(alpha+beta)^2-2alpha beta.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Roots of a Quadratic Equation.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
