The zeroes of the quadratic polynomial x² + kx + k, k ≠0
a. cannot both be positive
b. cannot both be negative
c. are always unequal
d. are always equal
Solution:
Given, the quadratic polynomial is x² + kx + k
We have to find the zeros of the polynomial
We know that, if 𝛼 and ꞵ are the zeroes of a polynomial ax^2 + bx + c, then
Sum of the roots is 𝛼 + ꞵ = -b/a
Product of the roots is 𝛼ꞵ = c/a
Where, a = coefficient of x² term
b = coefficient of x term
c = coefficient of constant term
Here, a = 1, b = k and c = k
Sum of the roots = -k/1
= -k
Product of the roots = k/1
= k
If k is negative,
Sum of the roots is positive
Product of the roots is negative.
So, one zero will be positive and other zero will be negative
If k is positive,
Sum of the roots is negative
Product of the roots is positive.
So, both the zeros will be negative.
Therefore, the zeros of the quadratic polynomial in both cases cannot be positive.
✦ Try This: The zeroes of the quadratic polynomial x² + nx + n, n ≠0 , a. cannot both be positive b. cannot both be negative c. are always unequal d. are always equal
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 2
NCERT Exemplar Class 10 Maths Exercise 2.1 Problem 8
The zeroes of the quadratic polynomial x² + kx + k, k ≠0, a. cannot both be positive, b. cannot both be negative, c. are always unequal, d. are always equal
Summary:
The zeroes of the quadratic polynomial x² + kx + k, k ≠0, cannot both be positive
☛ Related Questions:
visual curriculum