1
JEE Main 2022 (Online) 28th June Evening Shift
+4
-1

Let f(x) be a quadratic polynomial such that f($$-$$2) + f(3) = 0. If one of the roots of f(x) = 0 is $$-$$1, then the sum of the roots of f(x) = 0 is equal to :

A
$${{11} \over 3}$$
B
$${{7} \over 3}$$
C
$${{13} \over 3}$$
D
$${{14} \over 3}$$
2
JEE Main 2022 (Online) 28th June Morning Shift
+4
-1

The number of real solutions of

$${x^7} + 5{x^3} + 3x + 1 = 0$$ is equal to ____________.

A
0
B
1
C
3
D
5
3
JEE Main 2022 (Online) 27th June Morning Shift
+4
-1

The number of distinct real roots of x4 $$-$$ 4x + 1 = 0 is :

A
4
B
2
C
1
D
0
4
JEE Main 2022 (Online) 25th June Evening Shift
+4
-1

Let a, b $$\in$$ R be such that the equation $$a{x^2} - 2bx + 15 = 0$$ has a repeated root $$\alpha$$. If $$\alpha$$ and $$\beta$$ are the roots of the equation $${x^2} - 2bx + 21 = 0$$, then $${\alpha ^2} + {\beta ^2}$$ is equal to :

A
37
B
58
C
68
D
92
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