Qus : 10
2 The equation (x-a)3 +(x-b)3 +(x-c)3 = 0 has
1 All three real roots 2 One real and two imaginary roots 3 Three real roots,namely x = a, x = b, x = c 4 None of these Go to Discussion
Solution
Let f(x) = (x – a)3 + (x – b)3 + (x – c)3 .
Then f'(x) = 3{(x – a)2 + (x – b)2 + (x –c)2 }
clearly , f'(x) > 0 for all x.
so, f'(x) = 0 has no real roots.
Hence, f(x) = 0 has two imaginary and one real root
Qus : 11
4 Let
and
be the roots f the equation
and
are the roots of the equation
, then the value of r,
1 2 3 4 Go to Discussion
Solution
Qus : 12
4 If α≠β and $\alpha^2=5\alpha-3,\beta^2=5\beta-3$, then the equation whose roots are $\frac{\alpha}{\beta}$ and $\frac{\beta}{\alpha}$ is
1 $$3x^2-25x+3=0$$ 2 $$3x^2+5x+3=0$$ 3 $$3x^2-5x+3=0$$ 4 $$3x^2-19x+3=0$$ Go to Discussion
Solution Qus : 13
3 If $\alpha$ and $\beta$ are the roots of the equation $2x^{2}+ 2px + p^{2} = 0$, where $p$ is a non-zero real number, and $\alpha^{4}$ and $\beta^{4}$ are the roots of $x^{2} - rx + s = 0$, then the roots of $2x^{2} - 4p^{2}x + 4p^{4} - 2r = 0$ are:
1 Real and unequal 2 Equal and zero 3 Imaginary 4 Equal and non-zero Go to Discussion
Solution Qus : 14
3 If x and y are positive real numbers satisfying the system of equations $x^{2}+y\sqrt{xy}=336$ and $y^{2}+x\sqrt{xy}=112$, then x + y is:
1 $\sqrt{448}$ 2 $\sqrt{224}$ 3 20 4 40 Go to Discussion
Solution Qus : 15
3 The value of k for which the equation $(k-2)x^{2}+8x+k+4=0$
has both real, distinct and
negative roots is
1 0 2 2 3 4 4 -4 Go to Discussion
Solution Qus : 16
4 Roots of equation are $ax^2-2bx+c=0$ are n and m ,
then the value of $\frac{b}{an^2+c}+\frac{b}{am^2+c}$ is
1 c/a 2 b/a 3 a/c 4 b/c Go to Discussion
Solution Qus : 17
3 If a + b + c = 0, then the value of
1 1 2 0 3 3 4 -1 Go to Discussion
Solution Qus : 18
3 $a, b, c$ are positive integers such that $a^{2}+2b^{2}-2bc=100$ and $2ab-c^{2}=100$. Then the value of $\frac{a+b}{c}$ is
1 10 2 100 3 2 4 20 Go to Discussion
Solution Qus : 19
1 If $x^{2} + 2ax + 10 - 3a > 0$ for all x ∈ R, then
1 -5 2 a<-5 3 a>5 4 2 Go to Discussion
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Commented Apr 22 , 2022
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