Question

-5 is one of the zeroes of 2x²+px-15, zeroes of p(x²+x)+k are equal to each other. find the value of k.

Answer 1

Answer:

7 / 4

Step-by-step explanation:

 Here, - 5 is a root of the polynomial 2x^2 + px - 15, it means 2x^2 + px - 15 = 0 for x = - 5.

  When x = - 5

  ⇒ 2( - 5 )^2 + ( - 5 )p - 15 = 0

  ⇒ 2( 25 ) - 5p - 15 = 0

  ⇒ 50 - 5p - 15 = 0

  ⇒ 35 = 5p

  ⇒ 7 = p

Given, roots of p( x^2 + x ) + k[ px^2 + px + k ] are equal, therefore, discriminant of p( x^2 + x ) + k is 0.

 ⇒ discriminant = 0

 ⇒ p^2 - 4pk = 0

 ⇒ 7^2 - 4*7*k = 0

 ⇒ 49 - 28k = 0

 ⇒ 28k = 49

 ⇒ k = 49 / 28 = 7 / 4