Math, asked by ItzShrestha41, 6 hours ago

If 3 is a root of the quadratic equation x²-x+k=0, find the value of p so that the roots of the equation x²+k(2x+k+2)+p=0 are equal.


Solve it ASAP ^_^​

Answers

Answered by Anonymous
7

Given: 3 is a root of equation  {x}^{2}  - x  + k = 0

Substitute the value of x = 3

 {(3)}^{2}  - (3) + k = 0 \\ k =  - 6

Now ⇒{x}^{2} + k (2x - 6 + 2) + p = 0 \\⇒{x}^{2}  + ( - 6)(2x - 6 + 2) + p = 0 \\ ⇒{x}^{2}  - 12x + 36 - 12 + p = 0 \\ ⇒{x}^{2}  - 12x + (24 + p) = 0

Compare given equation with the general from of quadratic equation, which  {ax}^{2}  + bx + c = 0

⇒a = 1 ,b =  - 12, c = 24 + p

Find Discriminant:

D =  {b}^{2}  - 4ac \\   =  { - 12}^{2}  - 4  \times 1 \times (24 + p) \\  = 144 - 96 - 4p  \\ = 48 - 4p

Since roots are real and equal, put D=0

⇒48 - 4p = 0 \\ ⇒4p = 48 \\ ⇒p =  \frac{48}{4}  \\⇒p = 12

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