Question

if one zeros of quadratic polynomial of form x²+ac+b is negative of other then it's
(a) has no linear terms and constant term is negative
(b) has no linear term and constant term is positive
(c) can have a linear term but constant term is negative
(d) can have a linear term but constant term is positive
please explain step by step​

Answer 1

Answer:

(a) 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.

Step-by-step explanation:

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