Question

If a and B are the zeros of the polynomial f(x) = x2 -5x + k such that
a-B = 1, find the value of k.​

Answer 1

Hey there!

given α , β are zeroes of the polynomial f ( x).

Also, f ( x ) = x² - x - k.

We know that for a Quadratic polynomial, Sum of roots = - ( Coefficient of x) : Coefficient of x²

So,

α + β = - ( - 1) / 1 = 1

Also,

, from the question.

Solving the both equations, You would get

Now,

We know that,

Product of roots = 5 × - 4 = - 20

But, According to the given equation, Product of roots = - k.

Equating both of them,

-k = - 20

Therefore, The value of k is 20

hope it helps you