If one of the zeroes of a quadratic polynomial of the form x2 + ax + b

1.	If one of the zeroes of a quadratic polynomial of the form x2 + ax + b is the negative of the other, then itA. 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 liner term but the constant term is negative D. Can have a linear term but the constant term is positive
Answer» A. has no linear term and the constant term is negative Let p(x) = x² + ax + b And let α be one of the zeroes ∴ - α is the other zero of the polynomial p(x) Product of the zeroes = constant term ÷ coefficient of x² Product of the zeroes = b α(- α) = b - α² = b i.e. b is negative. Sum of the zeroes = - (coefficient of x) ÷ coefficient of x² α - α = - a 0 = - a ⇒ a = 0 ∴ The polynomials can be written as x² - α² (No linear term and negative constant term)

If one of the zeroes of a quadratic polynomial of the form x2 + ax + b is the negative of the other, then itA. 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 liner term but the constant term is negative D. Can have a linear term but the constant term is positive

Answer»

A. has no linear term and the constant term is negative

Let p(x) = x² + ax + b

And let α be one of the zeroes

∴ - α is the other zero of the polynomial p(x)

Product of the zeroes = constant term ÷ coefficient of x²

Product of the zeroes = b

α(- α) = b

- α² = b

i.e. b is negative.

Sum of the zeroes = - (coefficient of x) ÷ coefficient of x²

α - α = - a

0 = - a

⇒ a = 0

∴ The polynomials can be written as x² - α² (No linear term and negative constant term)