Question

if x = -2 is a root of the equation 3x² +7x+p=0 find the value of k so that the roots of the equation x² + k(4x+k-1) +p =0 are equal. (hint : p=2)
plz. answer as soon as possible.

Answer 1

since x=-2 is a root of 3x² +7x+p=0,  so put x=-2

⇒ 3× (-2)² + 7×(-2) +p =0

⇒12-14+p =0 ⇒ p = 14-12 = 2 ⇒ p = 2 ....... [1]

in x² + k(4x+k-1) +p =0 we have again the same zero i.e. -2, so put x=-2

⇒ (-2)²+k(4×(-2)+k-1)+p =0

⇒ 4+8k+k²-k+2 = 0    {  from [1] }

⇒k²+7k+6 = 0

⇒ k²+6k+k+6=0  (splitting)

⇒(k+6)(k+6) = 0 ⇒ k= -6