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Can the quadratic polynomial x² + kx + k have equal zeroes for some odd integer k > 1

Solution:

Given, the quadratic polynomial is x² + kx + k

We have to find whether the zeros of the polynomial are equal for some odd integer k > 1

Assuming the zeros of the polynomial are equal,

The value of the discriminant will be equal to zero.

b² - 4ac = 0

b² = 4ac

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

(k)² - 4(1)(k) = 0

k² - 4k = 0

k(k - 4) = 0

So, k = 0 or k = 4.

The quadratic polynomial will have equal zeros at k = 0 and k = 4

Therefore, the quadratic polynomial cannot have equal zeros for any odd integer k > 1

✦ Try This: Can the quadratic polynomial x² + ax + a have equal zeroes for some odd integer a > 1

Given, the quadratic polynomial is x² + ax + a

We have to find whether the zeros of the polynomial are equal for some odd integer a > 1

Assuming the zeros of the polynomial are equal,

The value of the discriminant will be equal to zero.

Discriminant = b² - 4ac

b² - 4ac = 0

b² = 4ac

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

a.² - 4(1)a. = 0

a² - 4a = 0

a(a - 4) = 0

So, a = 0 or a = 4.

The quadratic polynomial will have equal zeros at a = 0 and a = 4.

Therefore, the quadratic polynomial cannot have equal zeros for any odd integer a > 1

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

NCERT Exemplar Class 10 Maths Exercise 2.2 Problem 1 (v)

Summary:

The quadratic polynomial x² + kx + k has equal zeroes for some odd integer k > 1.Hence the statement is false.

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