Question
If one root of the equation ax2 + bx + c = 0 be n times the other root, then
Answer: Option B
:
B
Let the roots be α and nα
Sum of roots,α + nα = -ba⇒α = -ba(n+1) ......(i)
and product,α.n.α = ca⇒ α2 = cna ......(ii)
From (i) and (ii), we get
⇒ [ -ba(n+1) ]2 = cna⇒ b2a2(n+1)2 = cna
⇒ nb2 = ac(n+1)2.
Note : Students should remember this question as a fact.
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:
B
Let the roots be α and nα
Sum of roots,α + nα = -ba⇒α = -ba(n+1) ......(i)
and product,α.n.α = ca⇒ α2 = cna ......(ii)
From (i) and (ii), we get
⇒ [ -ba(n+1) ]2 = cna⇒ b2a2(n+1)2 = cna
⇒ nb2 = ac(n+1)2.
Note : Students should remember this question as a fact.
Was this answer helpful ?
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