0

Guest

Courses New

For a ≤ 0, determine all real roots of the equation x 2 – 2a | x –a | - 3a 2 = 0

For a ≤ 0, determine all real roots of the equation
x2 – 2a | x –a | - 3a2 = 0

Grade:upto college level

1 Answers

Navjyot Kalra
askIITians Faculty 654 Points
9 years ago
Sol. The given equation is,
X2 – 2a |x – a| - 3a2 = 0
Here two cases are possible
Case I : x – a > 0 then |x – a | = x – a
∴ Eq. Becomes
X2 – 2a(x – a) – 3a2 = 0
Or x2 – 2ax – a2 = 0 ⇒ x = 2a ± √4a2 + 4a2/2
⇒ x = a ± a√2
Case II : x – a < 0 then |x – a| = -(x – a)
∴ Eq. becomes
X2 + 2a(x – a) – 3a2 = 0
Or x2 + 2ax – 5a2 = 0
⇒ x = -2a ± √4a2 + 20a2/2
⇒ x = -2a ± 2a√6/2
x = -a ± a√6
Thus the solution set is { a ± a√2, -a ± a√6}

Think You Can Provide A Better Answer ?

Other Related Questions on Algebra

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More