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Question
The number of quadratic polynomials having zeroes –5 and –3 is ______.
Options
1
2
3
more than 3
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Solution
The number of quadratic polynomials having zeroes –5 and –3 is more than 3.
Explanation:
Let the zeroes of the polynomial be α and β
then, α = –5 and β = –3
The general form of the polynomial with zeroes α and β is given by:
k[x2 – (α + β)x + αβ], where k is any real number
= k[x2 – (–5 – 3)x + (–5)(–3)]
= k[x2 + 8x + 15]
Hence, more than 3 polynomials can have zeroes the –3 and –5.
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