Question

if roots of the equation 5x^2 + 2x + p(p-2)= 0 are of opposite sign then integral value of p is​

Answer 1

(4p−p

2

−5)x

2

−(2p−1)x+3p=0=f(x)

Roots lie on either side of unity.

∴f(1)>0 as (4p−p

2

−5<0)

⟹(4p−p

2

−5)1

2

−(2p−1)1+3p>0

⟹−p

2

+5p−4>0

⟹p

2

−5p+4<0

⟹(p−4)(p−1)<0

⟹p∈(1,4)

∴p=2,3

So two integral values of p.