Question

Find the values of p for which the equation (p+1)x^2 + 4px +9 = 0 has equal roots

Answer 1

ax^2+bx+c=0
for equal roots D=0
i.e b^2-4ac=0
here b= 4p
a=p+1
c=9
so
(4p)^2-4(p+1)9=0
16p^2-36p-36=0
divide whole equation by4
4p^2-9p-9=0
4p^2-12p+3p-9=0
4p(p-3)+3(p-3)=0
(4p+3)(p-3)=0
p=-3/4
or
p=3

Answer 2

thanks

Answer 3

welcome

Answer 4

Also, (b) Find the range of values of m for which the straight line y=mx-5 intesects the curve y=x^2-1 in two disctint points?

Answer 5

substitute y=mx-5 in the second equation, in last question we wanted only one root , here we need two distinct roots for that we need to have D>=0
mx-5=x^2-1
x^2-mx+4=0
ax^2+bx+c=0
D>0
b62-4ac>0
m^2-4*1*4>0
m^2-16>0
(m-4)(m+4)>0
either m<-4 or m.>4

Answer 6

wrote D>=0 it should be D>0, sorry :-|