Question

Find the value of P, if alpha, Beeta are roots of this equation, X2 -5x +P, alpha - Beeta = 1​

Answer 1

Answer :

The required value of P is 6.

Step-by-step explanation :

Given :

• α and β are the roots of the equation x² - 5x + P

• α - β = 1

To find :

the value of P

Solution :

To solve this question, we need to know the relation between roots and coefficients of quadratic equation.

• Sum of roots = -(x coefficient)/x² coefficient

• Product of roots = constant/x² coefficient

The given polynomial is x² - 5x + P.

x² coefficient = 1

x coefficient = -5

constant term = P

This question can be solved by using the sum of roots relation.

Using sum of roots relation :

• Since we are given the value of α - β , we'll find the value of α + β. Then we'll get the values of roots.

   sum of roots = -(x coefficient)/x² coefficient

   α + β = -(-5)/1

   α + β = 5 --[1]

   α - β = 1 --[2]

Add both the equations,

 α + β + α - β = 5 + 1

  2α = 6

    α = 6/2

    α = 3

One of the roots is 3.

Since it is a root of the given equation, when we put x = 3 the result is zero.

   3² - 5(3) + P = 0

  9 - 15 + P = 0

   -6 + P = 0

    P = 6

Therefore, the value of P is 6.