Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

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
6 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 ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free