If one of the zeroes of a quadratic polynomial of the form x² +ax + b is the negative of the other, then it
a. has no linear term and the constant term is negative
b. has no linear term and the constant term is positive
c. can have a linear term but the constant term is negative
d. can have a linear term but the constant term is positive
Solution:
Given, the quadratic polynomial is x² +ax + b.
One of the zeros of the polynomial is the negative of the other.
A quadratic polynomial in terms of the zeroes (α,β) is given by
x2 - (sum of the zeroes) x + (product of the zeroes)
i.e, f(x) = x2 -(α +β) x +αβ
Given, β = -α
So, sum of the zeros, α +β = α - α = 0
The coefficient of the x term will be zero.
Product of the roots, αβ = -α²
The constant term b will be negative.
Now, f(x) = x² - α²
Therefore, the quadratic polynomial has no linear term and the constant term is negative
✦ Try This: If one of the zeroes of a quadratic polynomial of the form x² + sx + t is the negative of the other, then it, a. has no linear term and the constant term is negative, b. has no linear term and the constant term is positive, c. can have a linear term but the constant term is negative, d. can have a linear term but the constant term is positive
Given, the quadratic polynomial is x² +sx + t.
One of the zeros of the polynomial is the negative of the other.
A quadratic polynomial in terms of the zeroes (α,β) is given by
x2 - (sum of the zeroes) x + (product of the zeroes)
i.e, f(x) = x2 -(α +β) x +αβ
Given, β = -α
So, sum of the zeros, α +β = α - α = 0
The coefficient of the x term will be zero.
Product of the roots, αβ = -α²
The constant term b will be negative.
Now, f(x) = x² - α²
Therefore, the quadratic polynomial has no linear term and the constant term is negative
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 2
NCERT Exemplar Class 10 Maths Exercise 2.1 Problem 10
If one of the zeroes of a quadratic polynomial of the form x² +ax + b is the negative of the other, then it, a. has no linear term and the constant term is negative, b. has no linear term and the constant term is positive, c. can have a linear term but the constant term is negative, d. can have a linear term but the constant term is positive
Summary:
If one of the zeroes of a quadratic polynomial of the form x² +ax + b is the negative of the other, then it has no linear term and the constant term is negative
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