Quadratic equation x 2- bx - c - has roots - and - such that LCM of - -24 and HCF of - -2 What is the total number of such quadratic equations if a and b are natural numbers-A- 4B- 1C- 2D- 3

The correct option is C 2HCF of α, β=2, so we can assume α = 2x and β = 2y. So, 2x× 2y = 24× 2, xy = 12. Different values of x and y possible are (12, 1), (4, ...

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Question

Quadratic equation $x^{2} + b x + c =$ has roots $α a n d β$ , such that LCM of $(α, β)$ = 24 and HCF of $(α, β)$ = 2.
What is the total number of such quadratic equations if a and b are natural numbers?

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Solution

The correct option is B 2
HCF of $α, β = 2$ , so we can assume $α = 2 x$ and $β = 2 y$ .
So, $2 x \times 2 y = 24 \times 2$ , xy = 12.
Different values of x and y possible are (12, 1), (4, 3) and hence different values of roots of the equation will be (24, 2), (8, 6).

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Quadratic equation x2+bx+c= has roots α and β, such that LCM of (α,β) = 24 and HCF of (α,β) = 2. What is the total number of such quadratic equations if a and b are natural numbers?

The correct option is B 2HCF of α,β=2, so we can assume α=2x and β=2y. So, 2x×2y=24×2, xy = 12. Different values of x and y possible are (12, 1), (4, 3) and hence different values of roots of the equation will be (24, 2), (8, 6).

Quadratic equation $x^{2} + b x + c =$ has roots $α a n d β$ , such that LCM of $(α, β)$ = 24 and HCF of $(α, β)$ = 2.
What is the total number of such quadratic equations if a and b are natural numbers?

The correct option is B 2
HCF of $α, β = 2$ , so we can assume $α = 2 x$ and $β = 2 y$ .
So, $2 x \times 2 y = 24 \times 2$ , xy = 12.
Different values of x and y possible are (12, 1), (4, 3) and hence different values of roots of the equation will be (24, 2), (8, 6).