Question

. 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.​

Answer 1

A

Step-by-step explanation:

when one zero is negative of the other then there is no (b) term which is linear term.

and also when we multiply both the zeroes we get negative value so the term ( c) of ax^2 + bx + c is negative..

Answer 2

Answer:

(a) has no linear term and the constant term is negative.

Step-by-step explanation:

Let p(x) = x2 + ax + b.

Put a = 0, then, p(x) = x2 + b = 0

⇒ x2 = -b

⇒ x = ± ±√-b

[∴b < 0]

Hence, if one of the zeroes of quadratic polynomial p(x) is the negative of the other, then it has no linear term i.e., a = O and the constant term is negative i.e., b< 0.

Alternate Method

Let f(x) = x2 + ax+ b

and by given condition the zeroes area and – α.

Sum of the zeroes = α- α = a

=>a = 0

f(x) = x2 + b, which cannot be linear,

and product of zeroes = α .(- α) = b

⇒ -α2 = b

which is possible when, b < 0.

Hence, it has no linear term and the constant term is negative.