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The only value of k for which the quadratic polynomial kx² + x + k has equal zeros is 1/2. Is the statement true or false? Justify your answer

Solution:

Given, the quadratic polynomial is kx² + x + k.

We have to find the value of k for which the quadratic polynomial has equal zeros as 1/2.

Assuming the zeros of the polynomial are equal, the value of the discriminant will be equal to zero.

Discriminant = b² - 4ac

b² - 4ac = 0

Here, a = k, b = 1 and c = k

(1)² - 4(k)(k) = 0

1 - 4k² = 0

4k² = 1

k² = 1/4

Taking square root,
k = ±1/2

Therefore, the quadratic polynomial has equal zeros for k = ±1/2.

✦ Try This: The only value of a for which the quadratic polynomial ax² + x + a has

equal zeros is 1/2. Is the statement true or false? Justify your answer

Given, the quadratic polynomial is ax² + x + a.

We have to find the value of k for which the quadratic polynomial has equal zeros as 1/2.

Assuming the zeros of the polynomial are equal, the value of the discriminant will be equal to zero.

Discriminant = b² - 4ac

b² - 4ac = 0

Here, a = a, b = 1 and c = a

(1)² - 4a.a. = 0

1 - 4a² = 0

4a² = 1

a² = 1/4

a = ±1/2

Therefore, the quadratic polynomial has equal zeros for a = ±1/2.

The only value of a for which the quadratic polynomial ax² + x + a has

equal zeros is 1/2.

Therefore, the statement is false

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 2

NCERT Exemplar Class 10 Maths Exercise 2.2 Problem 2 (vii)

Summary:

The only value of k for which the quadratic polynomial kx² + x + k has equal zeros is 1/2. The statement is false

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