If α, β are the roots of the equation ax2 + bx + c = 0 such that β

Question

If α, β are the roots of the equation ax2 + bx + c = 0 such that β < α < 0, then the quadratic equation whose roots are |α|, |β|, is given by (A) |a| x2 + |b| x + |c| = 0 (B) ax2 - |b| x + c = 0 (C) |a| x2 - |b| x + |c| = 0 (D) a|x|2 + b|x| + |c| = 0

Tardigrade Admin · Accepted Answer

Since, α and β be the roots of the equation ax2 + bx + c = 0, then α + β = -(b/a) and αβ = (c/a) Now, sum of roots = |α|+|β| = -α - β (∵ β < α < 0) = -(-(b/a)) = |(b/a)| (∵ |α |+|β | > 0) and product of roots = |α ||β | = |(c/a)| Hence, required equation is x2-|(b/a)|x+|(c/a)| = 0 ⇒ |a| x2 - |b| x + |c| = 0

Q. If $α, β$ are the roots of the equation $a x^{2} + b x + c = 0$ such that $β < α < 0$ , then the quadratic equation whose roots are $∣ α ∣, ∣ β ∣$ , is given by

$∣ a ∣ x^{2} + ∣ b ∣ x + ∣ c ∣ = 0$

$a x^{2} - ∣ b ∣ x + c = 0$

$∣ a ∣ x^{2} - ∣ b ∣ x + ∣ c ∣ = 0$

$a ∣ x ∣^{2} + b ∣ x ∣ + ∣ c ∣ = 0$

Q. If α,β are the roots of the equation ax2+bx+c=0 such that β<α<0, then the quadratic equation whose roots are ∣α∣,∣β∣, is given by

∣a∣x2+∣b∣x+∣c∣=0

ax2−∣b∣x+c=0

∣a∣x2−∣b∣x+∣c∣=0

a∣x∣2+b∣x∣+∣c∣=0

Q. If $α, β$ are the roots of the equation $a x^{2} + b x + c = 0$ such that $β < α < 0$ , then the quadratic equation whose roots are $∣ α ∣, ∣ β ∣$ , is given by

$∣ a ∣ x^{2} + ∣ b ∣ x + ∣ c ∣ = 0$

$a x^{2} - ∣ b ∣ x + c = 0$

$∣ a ∣ x^{2} - ∣ b ∣ x + ∣ c ∣ = 0$

$a ∣ x ∣^{2} + b ∣ x ∣ + ∣ c ∣ = 0$