If α and ß are the roots of the equation ax2 + bx + c = 0, then find the roots of the equation ab2x2 + b2cx + c3 = 0
Explanation:
Dividing the equation ab2x2 + b2cx + c3 = 0 by c2, we get
abxc2 + bbxc + c = 0
Since α and ß are roots of ax2 + bx + c = 0
∴ bxc = α or ß
⇒ x = cbα or cbß
Now, we know α + ß = -b/a and αß = c/a Dividing both equations, we get ⇒ cb = - αßα+ß
⇒ x = cbα =-α2ßα+ß or cbß = -αß2α+ß
Hence, -α2ßα+ß and -αß2α+ß are the roots of the equation ab2x2 + b2cx + c3 = 0.
Hence, option (a).
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