Question

if alpha, beta are zeros of p(x)= x³-5x+k and alpha - beta= 1 then find k

Answer 1

Heya !!!

I think there is a mistake in your question.

Polynomial should be P(X) = X²-5X+K

P(X) => X²-5X+K

Here,

A = 1 , B = -5 and C = K

Alpha + Beta = -B/A

Alpha + Beta = -(5)/1

Alpha + Beta = 5 --------(1)

And,

Alpha - Beta = 1 ----------(2)

From equation (1) we get,

Alpha + Beta = 5

Alpha = 5- Beta ---------(3)

Putting the value of Alpha in equation (2)

Alpha - Beta = 1

5 - Beta - Beta = 1

-2Beta = 1-5

-2Beta = -4

Beta = -4/-2 => 2

Putting the value of Beta in equation (3)

Alpha = 5 - Beta

Alpha = 5-2 = 3

Product of zeroes = C/A

Alpha × Beta = K/1

3 × 2 = K /1

K = 6

HOPE IT WILL HELP YOU...... :-)