If c(\alphac) and c(\betac) are the roots of the equation c(x^2-6x+2=0c), what is the value of c(\alpha^2+\beta^2c)?
Answer and explanation
Correct answer: 32
For the quadratic equation c(x^2-6x+2=0c), the sum of the roots is c(\alpha+\beta=6c) and their product is c(\alpha\beta=2c). Using the identity c(\alpha^2+\beta^2=(\alpha+\beta)^2-2\alpha\betac), we get c(\alpha^2+\beta^2=6^2-2(2)=36-4=32c). Therefore, option A is correct. Exam tip: use c(\alpha^2+\beta^2=(\alpha+\beta)^2-2\alpha\betac); 36 is only c((\alpha+\beta)^2c), not the required value.
Frequently asked questions
What is the correct answer to this question?
32
Why is this the correct answer?
For the quadratic equation c(x^2-6x+2=0c), the sum of the roots is c(\alpha+\beta=6c) and their product is c(\alpha\beta=2c). Using the identity c(\alpha^2+\beta^2=(\alpha+\beta)^2-2\alpha\betac), we get c(\alpha^2+\beta^2=6^2-2(2)=36-4=32c). Therefore, option A is correct. Exam tip: use c(\alpha^2+\beta^2=(\alpha+\beta)^2-2\alpha\betac); 36 is only c((\alpha+\beta)^2c), not the required value.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Roots of a Quadratic Equation.
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