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Question
A quadratic polynomial, the sum of whose zeroes is 0 and one zero is 3, is
Options
x2 − 9
x2 + 9
x2 + 3
x2 − 3
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Solution
Since `alpha ` and `beta` are the zeros of the quadratic polynomials such that
`0 = alpha + beta`
If one of zero is 3 then
`alpha + beta =0`
`3 + beta = 0`
`beta = 0 -3`
`beta =-3`
Substituting `beta =-3` in `alpha + beta =0` we get
`alpha -3 =0`
`alpha =3`
Let S and P denote the sum and product of the zeros of the polynomial respectively then
`S = alpha+ beta`
`S = 0`
`P = alphabeta`
`P = 3xx-3`
` P = -9`
Hence, the required polynomials is
`= (x^2 - Sx + p)`
`= (x ^2 - 0x- 9)`
`= x^2 - 9`
Hence, the correct choice is `(a).`
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