Question Number 11500 by @ANTARES_VY last updated on 27/Mar/17

(x^2 +x−4)(x^2 +x+4)=9  find  the  equation  has  multiple  roots.

Answered by ridwan balatif last updated on 27/Mar/17

((x^2 +x)−4)((x^2 +x)+4)=9  (x^2 +x)^2 −16=9  (x^2 +x)^2 −25=0  ((x^2 +x)−5)((x^2 +x)+5)=0  (i) x^2 +x−5=0  D=b^2 −4ac      =1^2 −4(1)(−5)      =21  x_(1,2) =((−b±(√D))/(2a))          =((−1±(√(21)))/2)  x_1 =((−1+(√(21)))/2)  x_2 =−(((1+(√(21)))/2))  (ii) x^2 +x+5=0  D=b^2 −4ac      =1^2 −4(1)(5)      =−19 (IMPOSSIBLE)  point (ii) has no roots

Commented by@ANTARES_VY last updated on 27/Mar/17

The  answer  is: −5.

Commented by@ANTARES_VY last updated on 27/Mar/17

error

Commented bymrW1 last updated on 27/Mar/17

please explain what you mean with  your question.

Commented bymrW1 last updated on 27/Mar/17

then your question should be: find the  product of the real roots of the  equation.

Commented by@ANTARES_VY last updated on 27/Mar/17

x_1 ×x_2 =?

Commented bymrW1 last updated on 27/Mar/17

yes.  x_1 ×x_2 =−5

Commented bysandy_suhendra last updated on 27/Mar/17

from the answer of Mr Ridwan Balatif  x^2 +x+5=0 has 2 imaginary roots because D<0  x^2 +x−5=0 has 2 real roots x_1  and x_2  because D>0       so x_1 .x_2  = (c/a) = ((−5)/1) = −5

Answered by ajfour last updated on 27/Mar/17

x=((−1±(√(1±20)))/2) .