If (\alpha, \beta) are the roots of the equation (x^2-9x+20=0) , what is the value of (\alpha-4)(\beta-4) ?
Answer and explanation
Correct answer: 0
By Vieta’s formulas, \alpha+\beta=9 and \alpha\beta=20 . Therefore, (\alpha-4)(\beta-4)=\alpha\beta-4(\alpha+\beta)+16=20-4(9)+16=0 . Hence, option A is correct. Choosing 4 or -16 usually results from omitting the middle term -4(\alpha+\beta) during expansion. Exam tip: for (ax^2+bx+c=0) , the sum of roots is -b/a and their product is c/a .
Frequently asked questions
What is the correct answer to this question?
0
Why is this the correct answer?
By Vieta’s formulas, \alpha+\beta=9 and \alpha\beta=20 . Therefore, (\alpha-4)(\beta-4)=\alpha\beta-4(\alpha+\beta)+16=20-4(9)+16=0 . Hence, option A is correct. Choosing 4 or -16 usually results from omitting the middle term -4(\alpha+\beta) during expansion. Exam tip: for (ax^2+bx+c=0) , the sum of roots is -b/a and their product is c/a .
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Introduction to Quadratic Equations.
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