Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively. (i) (ii) (iii) (iv) 1, 1 (v) (vi)

Question

Philoid · Accepted Answer

(i) , -1

Let the polynomial be , and its zeroes be .

If a = 4, then b = -1, c = -4

Therefore, the quadratic polynomial is 4x² − x − 4.

(ii)

Let the polynomial be , and its zeroes be

If a = 3, then b = , c = 1

Therefore, the quadratic polynomial is

(iii) 0,

Let the polynomial be , and its zeroes be

If a = 1, then b = 0, c =

Therefore, the quadratic polynomial is .

(iv) 1, 1

Let the polynomial be , and its zeroes be

If a = 1, then b = -1, c = 1

Therefore, the quadratic polynomial is .

(v)

Let the polynomial be , and its zeroes be

If a = 4, then b = 1, c = 1

Therefore, the quadratic polynomial is .

(vi) 4, 1

Let the polynomial be and its zeroes be

If a = 1, then b = -4, c = 1

Therefore, the quadratic polynomial is .