Banner 0
Banner 1
Banner 2
Banner 3
Banner 4
Banner 5
Banner 6
Banner 7
Banner 8
Banner 9

Q.

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

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.
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

JEE

NEET

NEET

Foundation JEE

Foundation JEE

Foundation NEET

Foundation NEET

CBSE

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
Watch 3-min video & get full concept clarity
score_test_img

courses

No courses found

Get Expert Academic Guidance – Connect with a Counselor Today!

whats app icon
personalised 1:1 online tutoring