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Question
A quadratic polynomial, whose zeroes are –3 and 4, is ______.
Options
`x^2 - x + 12`
`x^2 + x + 12`
`x^2/2 - x/2 - 6`
`2x^2 + 2x - 24`
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Solution
A quadratic polynomial, whose zeroes are –3 and 4, is `underlinebb(x^2/2 - x/2 - 6)`.
Explanation:
Sum of zeroes, α + β = –3 + 4 = 1
Product of zeroes, αβ = –3 × 4 = –12
Therefore, the quadratic polynomial becomes,
x2 – (sum of zeroes)x + (product of zeroes)
= x2 – (α + β)x + (αβ)
= x2 – (1)x + (–12)
= x2 – x – 12
Divide by 2, we get
= `x^2/2 - x/2 -12/2`
= `x^2/2 - x/2 - 6`
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