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Question
The number of polynomials having zeroes as –2 and 5 is ______.
Options
1
2
3
More than 3
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Solution
The number of polynomials having zeroes as –2 and 5 is more than 3.
Explanation:
According to the question,
The zeroes of the polynomials = –2 and 5
We know that the polynomial is of the form,
p(x) = ax2 + bx + c.
Sum of the zeroes = – (Coefficient of x) ÷ Coefficient of x2 i.e.
Sum of the zeroes = – `b/a`
– 2 + 5 = `– b/a`
3 = `– b/a`
b = – 3 and a = 1
Product of the zeroes = Constant term ÷ Coefficient of x2 i.e.
Product of zeroes = `c/a`
(–2)5 = `c/a`
– 10 = c
Substituting the values of a, b and c in the polynomial p(x) = ax2 + bx + c.
We get, x2 – 3x – 10
Therefore, we can conclude that x can take any value.
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