If `x = alpha`, is a zero of a polynomial then `x -alpha `is a factor of `f(x)`
Since 3 is the zero of the polynomial , f(x) = x2 − 5x + 4,
Therefore `x - 3`is a factor of `f(x)`
Now, we divide`f(x) = x^2 - 5x + 4 ` by `(x - 3)` we get
Therefore we should add 2 to the given polynomial
Hence, the correct choice is (b).
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What should be subtracted to the polynomial x2 − 16x + 30, so that 15 is the zero of the resulting polynomial?
We know that, if `x = alpha`, is zero of a polynomial then `x-alpha` is a factor of f(x)
Since 15 is zero of the polynomial f (x) = x2 − 16x + 30, therefore (x − 15) is a factor of f (x)
Now, we divide f(x) = x2 − 16x + 30 by ( x - 15) we get
Thus we should subtract the remainder 15 from `x^2 - 16x+30`
Hence, the correct choice is (c).
Concept: Relationship Between Zeroes and Coefficients of a Polynomial
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What number should be added to polynomial x2 5x+4 so that 3 is the zero of polynomial?
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