Question

Find a quadratic polynomial, the sum of where zues is 0 and
one zero is 5
​

Answer 1

Let the zeros of quadratic polynomial be a and b

given that sum of zeroes is 0

=> a + b = 0

It is also given that one of the zero is 5

, let say a = 5 ,

Now as a + b = 0

=> 5 + b = 0 => b = -5

Thus zeros are a = 5 and b = -5

Quadratic Polynomial whose zeroes are a and b is given by

$p(x) = k( {x}^{2} - (sum \: of \: zeroes)x + (product \: of \: zeroes) \\ = k( {x}^{2} - (a + b)x + ab) \\ = k( {x}^{2} - 0 \: x \: + 5( - 5)) \\ = k( {x}^{2} - 25)$

where k is any real number