If roots of x^2-(a+2)x+2a=0 are 2 and a, which reason is correct?
Answer and explanation
Correct answer: Sum is (a+2) and product is (2a)
For a monic quadratic x^2+bx+c=0 with roots r and s, Vieta’s relations give r+s=-b and rs=c. Here the coefficient of x is -(a+2), so the sum of the roots is -[-(a+2)]=a+2. The constant term is 2a, so their product is 2a. Taking the stated roots r=2 and s=a gives the same results directly: r+s=2+a and rs=2a. Thus option A correctly identifies both relationships. Equal roots are not guaranteed, and the discriminant is not always negative; in fact, the equation factors as (x-2)(x-a)=0.
Frequently asked questions
What is the correct answer to this question?
Sum is (a+2) and product is (2a)
Why is this the correct answer?
For a monic quadratic x^2+bx+c=0 with roots r and s, Vieta’s relations give r+s=-b and rs=c. Here the coefficient of x is -(a+2), so the sum of the roots is -[-(a+2)]=a+2. The constant term is 2a, so their product is 2a. Taking the stated roots r=2 and s=a gives the same results directly: r+s=2+a and rs=2a. Thus option A correctly identifies both relationships. Equal roots are not guaranteed, and the discriminant is not always negative; in fact, the equation factors as (x-2)(x-a)=0.
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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