1
WB JEE 2012
MCQ (Single Correct Answer)
+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
2
WB JEE 2024
MCQ (Single Correct Answer)
+1
-0.25
Change Language

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
3
WB JEE 2024
MCQ (Single Correct Answer)
+1
-0.25
Change Language

Let $$\mathrm{N}$$ be the number of quadratic equations with coefficients from $$\{0,1,2, \ldots, 9\}$$ such that 0 is a solution of each equation. Then the value of $$\mathrm{N}$$ is

A
29
B
39
C
90
D
81
4
WB JEE 2024
MCQ (Single Correct Answer)
+1
-0.25
Change Language

If $$a, b, c$$ are distinct odd natural numbers, then the number of rational roots of the equation $$a x^2+b x+c=0$$

A
must be 0
B
must be 1
C
must be 2
D
cannot be determined from the given data
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