What number should be added to the polynomial x 2 − 5x 4 so that 3 is a zero of polynomial so obtained?

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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