Question
If x2+ax+10=0 and x2+bx−10=0 have a common root, then a2−b2 is equal to
Answer: Option D
:
D
Letα be a common root, then
α2+αα+10=0
and α2+bα−10=0
from (i) - (ii),
(a−b)α+20=0⇒α = −20a−b
Substituting the value ofα in (i), we get
(−20a−b)2+a(−20a−b)+10=0
⇒400 - 20 a(a - b) + 10(a−b)2 = 0
⇒40 -2a2 + 2ab +a2 +b2 -2ab = 0
⇒a2 -b2 = 40
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:
D
Letα be a common root, then
α2+αα+10=0
and α2+bα−10=0
from (i) - (ii),
(a−b)α+20=0⇒α = −20a−b
Substituting the value ofα in (i), we get
(−20a−b)2+a(−20a−b)+10=0
⇒400 - 20 a(a - b) + 10(a−b)2 = 0
⇒40 -2a2 + 2ab +a2 +b2 -2ab = 0
⇒a2 -b2 = 40
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