1
WB JEE 2011
+1
-0.25

If the ratio of the roots of the equation $$p{x^2} + qx + r = 0$$ is $$a:b$$, then $${{ab} \over {{{(a + b)}^2}}}$$ =

A
$${{{p^2}} \over {qr}}$$
B
$${{pr} \over {{q^2}}}$$
C
$${{{q^2}} \over {pr}}$$
D
$${{pq} \over {{r^2}}}$$
2
WB JEE 2011
+1
-0.25

If $$\alpha$$ and $$\beta$$ are the roots of the equation x2 + x + 1 = 0, then the equation whose roots ar $$\alpha$$19 and $$\beta$$7 is

A
x2 $$-$$ x $$-$$ 1 = 0
B
x2 $$-$$ x + 1 = 0
C
x2 + x $$-$$ 1 = 0
D
x2 + x + 1 = 0
3
WB JEE 2012
+2
-0.67
The quadratic equation 2x2 $$-$$ (a3 + 8a $$-$$ 1)x + a2 $$-$$ 4a = 0 possesses roots of opposite sign. Then,
A
a $$\le$$ 0
B
0 < a < 4
C
4 $$\le$$ a $$\le$$ 8
D
a $$\ge$$ 8
4
WB JEE 2024
+1
-0.25

If $$\mathrm{P}(x)=\mathrm{a} x^2+\mathrm{b} x+\mathrm{c}$$ and $$\mathrm{Q}(x)=-\mathrm{a} x^2+\mathrm{d} x+\mathrm{c}$$ where $$\mathrm{ac} \neq 0$$, then $$\mathrm{P}(x) \cdot \mathrm{Q}(x)=0$$ has (a, b, c, d are real)

A
2 real roots
B
at least two real roots
C
4 real roots
D
no real root
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