In writing an equation of the form ax2+bx+c=0;the coefficient of x is written incorrectly and roots are found to be equal. Again, io writing the same equation the constant term is written incorrectly and it is found that one root is equal to those of the previous wrong equation while the other is double of it. If α and β be the roots of correct equation, then (α−β)2 is equal to
see full answer
High-Paying Jobs That Even AI Can’t Replace — Through JEE/NEET
🎯 Hear from the experts why preparing for JEE/NEET today sets you up for future-proof, high-income careers tomorrow.
An Intiative by Sri Chaitanya
a
5
b
5αβ
c
-4αβ
d
-4
answer is B.
(Unlock A.I Detailed Solution for FREE)
Best Courses for You
JEE
NEET
Foundation JEE
Foundation NEET
CBSE
Detailed Solution
Let the correct equation is ax2+bx+c=0then α+β=−ba and αβ=caWhen b is written incorrectly, then the roots are equal.Let these are y and Y∴ γ⋅γ=ca⇒γ2=αβ ........(i)When c is written incorrectly, then the roots are y and 2y. ∴ γ+2γ=−ba⇒3γ=α+β⇒ 9γ2=(α+β)2⇒9αβ=(α−β)2+4αβ [from Eq. (i)] ∴ (α,−β)2=5αβ