25. If one of the zeroes …
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Gaurav Seth 5 years, 2 months ago
it has no linear term and the constant term is negative.
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.
2Thank You