Question

Assertion(A): If both zeros of the quadratic polynomial x² - 2kx +2 in magnitude but opposite in sign then value of k is 1/2

Reason(R): Sum of zeros of a quadratic polynomial ax² +bx+c is-b/a

a) If both the assertion and the reason are true and the reason is a correct explanation of the assertion.
b) If both the assertion and reason are true but the reason is not a correct explanation of the assertion
c) Assertion is true but reason is false
d) Assertion is false but reason is true​

Answer 1

Answer:

c)Assertion is false but reason is true

Step-by-step explanation:

p(x)=x^2-2kx, (here a=1,b=-2k,c=0)

let zeroes are alpha and beta

A.T.Q.

alpha= -beta. eq.1

Sum of zeroes =-b/a

alpha + beta = -(-2k)/1

-beta+beta=2k (from eq.1)

0=2k

k=0/2=0

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Answer 2

Given :  Assertion(A): If both zeros of the quadratic polynomial x² - 2kx +2 equal in magnitude but opposite in sign then value of k is 1/2

Reason(R): Sum of zeros of a quadratic polynomial ax² +bx+c is -b/a

To Find : Comment on Assertion and Reason

Solution:

Reason(R): Sum of zeros of a quadratic polynomial ax² +bx+c is  -b/a

Reason is TRUE

Assertion(A): If both zeros of the quadratic polynomial x² - 2kx +2 in magnitude but opposite in sign then value of k is 1/2

x² - 2kx +2

zeros of the quadratic polynomial  equal in magnitude but opposite in sign

Hence sum of zeroes = 0

Sum of zeroes = - (-2k)/1  = 2k

Equate Sum of zeroes

=> 2k = 0

=> k = 0

Hence k ≠ 1/2

so Assertion is False

Correct option is d)  Assertion is false but reason is true​

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