Question

( frac{x^{2}+2 x+a}{x^{2}+4 x+3 a} ) can take all values if ( x^{2}+4 x+3 a eq 0 )
tef
( Rightarrow quad x^{2}+4 x+3 a eq 0 quad Rightarrow quad D>0 )
( 2 times 2 times 230 times 2 times 28 )
[
4^{2}-4(3 a) 70^{0}
]
( 12 a<16 a a^{2}<4 / 3 )
So for ( a in(-infty, 4 / 3) )
eq ( ^{n} ) can tate all real values.

# can take all real values if x2 + 2x + a 13 H x = R then. x? + 4x + 3a (1) a € (0, 2) (3) a E (-1, 1) (2) a € (0, 1) (4) None of these ? + hy + c = 0 are real and of a in

Solution