If the sum of the roots of the equation (x - p)(2x - 1)=0 is 1, find the value of p

 Option

(i)3/2

(ii)1/2(✔️)

(iii) -3/2

(iv) -1/2

Solution

let 𝛼 and ꞵ root of the Quadratic Equation

(x - p)(2x - 1)=0

⇒x (2x - 1)- p (2x - 1)=0 

⇒2x^2 -x- 2px - p=0 

⇒2x^2 -x(1+2p) - p=0  

Here, a=2 , b = -(1+2p) and c=-p

According to Question,

𝛼 + ꞵ = 1

-b/a =1

-{-(1+2p)}/2 = 1

+(1+2p)/2 = 1

1+2p =2

2p =2 - 1

2p=1

p=1/2

 

 

 

 

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