Question

If 3 is a root of the quadratic equations X2 - X + k =0,find the value of p so that the roots of the equation X2+k(2x+k+2)+p =0are equal

Answer 1

Answer:

If 3 is a root of the equation x^2 - x +k =0

So putting the value = 3 in equation...

3^2 - 3 + k = 0

9 - 3 + k = 0

6 + k = 0

K = - 6

If the roots of equation are real and equal..

b^2 - 4*a*c = 0....... (Eq. 1)

Eq. = x^2 + k (2x+k+2)+p = 0. ____ (putting the value of k)...

x^2 +(-6)(2x+(-6)+2)+p=0

x^2-6(2x-4)+p = 0

x^2 - 12x + 24 + p = 0

ax^2 +bx +c = 0...

a = 1

b = - 12

c = 24 + p

So put the value of a, b and c in ( Eq. 1)

-12^2- 4*1*(24 + p) = 0

144 - 4(24 + p) = 0

144 - 96 - 4p = 0

48 - 4p = 0

-4p = - 48

P = - 48/-4

p = 12.... ans...

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