Question

2) Find a quadratic polynomial with the sum and product of zeroes are 1/4 and - 1/4 respectively.​

Answer 1

Answer:

4x²- x - 1 = 0.

Step-by-step explanation:

let the polynomial be ax² + bx + c = 0

dividing by a on both sides

we get x²+ (b/a)x + c/a = 0

and

let m and n be the zeros of the quadratic polynomial

==> m+n = -b/a = 1/4, b/a = -1/4

==> mn = c/a = -1/4

==> hence the polynomial is given by

x² + (-1/4)x + (-1/4) = 0

multiplying 4 on bith sides we get

4x²- x - 1 = 0.