Question

Assertion : If alpha & Beta are zeroes of polynomial x²-8x+1 then value of 1/alpha + 1/beta is equals to 11.
Reason : If alpha & Beta are zeroes of Quadratic polynomial ax² + bx + c, then alpha + beta = -b/a AND alpha×beta = c/a.


Explain with proper Pen & paper solving.
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Answer 1

Answer:

Reason : If alpha & Beta are zeroes of Quadratic polynomial ax² + bx + c, then alpha + beta = -b/a AND alpha×beta = c/a.

Answer 2

Given : Assertion : If α & β are zeroes of polynomial x²-8x+1 then value of 1/α + 1/β is equals to 11.

Reason : If α & β are zeroes of Quadratic polynomial ax² + bx + c, then α + β = -b/a AND α×β = c/a.

To Find : Comments on Assertion and Reason

Solution:

Assertion : If α & β are zeroes of polynomial x²-8x+1 then value of 1/α + 1/β is equals to 11.

Sum of zeroes = α +  β = -(-8)/1 = 8

Product of zeroes = αβ = 1/1 = 1

1/α + 1/β   = (β + α)/αβ   =  8/1  = 8

Hence  1/α + 1/β ≠ 11

so Assertion is False

Reason : If α & β are zeroes of Quadratic polynomial ax² + bx + c, then α + β = -b/a and  α×β = c/a.

polynomial ax² + bx + c

Sum of zeroes = α +  β  = -b/a

Product of zeroes = αβ = c/a

Reason is TRUE

Assertion is False and Reason is TRUE

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