Hey there! We receieved your request
Stay Tuned as we are going to contact you within 1 Hour
One of our academic counsellors will contact you within 1 working day.
Click to Chat
1800-5470-145
+91 7353221155
Use Coupon: CART20 and get 20% off on all online Study Material
Complete Your Registration (Step 2 of 2 )
Sit and relax as our customer representative will contact you within 1 business day
OTP to be sent to Change
The quadratic equations x2 - 6x + a = 0 and x2 - cx + 6 = 0 have one root in common. The other roots of the first and second equations are integers in the ratio 4 : 3. Then what is the common root?
Let α and β are roots of: x2 - 6x + a = 0 Let α and γ are roots of: x2 - cx + 6 = 0 So, α + β = 6 ........ (i) α.β = a ........ (ii)
α + γ = c ........ (iii) α.γ = 6 ........ (iv)
β/γ = 4/3 ........ (v)
Now using (ii) and (iii) α.β/α.γ = a/6 => β/γ = a/6 => using (v), 4/3 = a/6 => So, a = 8
Now , x2 - 6x + a = 0 x2 - 6x + 8 = 0 x = 2 OR 6 As α.β = 8 So α = 2
Register Yourself for a FREE Demo Class by Top IITians & Medical Experts Today !