Question

If a, B are zeros of ax2 + bx + c then zeros of a3x2 + abcx + c3 are:-​

Answer 1

Given : α , β are zeroes of quadratic polynomial , ax² + bx + c.

To find : zeroes of a³x² + abcx + c³ are ....

solution : α , β are zeroes of quadratic polynomial , ax² + bx + c.

sum of zeroes = α + β = -b/a . ........(1)

product of zeroes = αβ = c/a .........(2)

let α' and β' are the zeroes of polynomial, a³x² + abcx + c³

sum of zeroes = α' + β' = -abc/a³ = -bc/a²

= (-b/a) × (c/a)

from equations (1) and (2) we get,

= (α + β)αβ = α²β + αβ² .........(3)

product of zeroes = α'β' = c³/a³

= (c/a)³

= (αβ)³ = α³β³ .......(4) [from eq (2) .]

from equations (3) and (4) we get,

α' = α²β and β' = αβ²

Therefore the zeroes of a³x² + abcx + c³ are α²β and αβ²

Answer 2

Answer:

yes this is the correct answer