JEE MAIN Quadratic Equations Previous Year Questions (PYQs) – Page 1 of 8
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The number of real solutions of the equation, x2 $-$ |x| $-$ 12 = 0 is :
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Solution
Let a , b, c , d and p be any non zero distinct real numbers such that(a2 + b2 + c2)p2 – 2(ab + bc + cd)p + (b2 + c2 + d2) = 0. Then :
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Solution
The minimum value of the sum of the squares of the roots of
$x^{2}+(3-a)x+1=2a$ is:
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Solution
If $\alpha $ and $\beta $ be two roots of the equation x2 – 64x + 256 = 0. Then the value of${\left( {{{{\alpha ^3}} \over {{\beta ^5}}}} \right)^{1/8}} + {\left( {{{{\beta ^3}} \over {{\alpha ^5}}}} \right)^{1/8}}$ is :
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Solution
The value of $\lambda$ such that the sum of the squares of the roots of the quadratic equation
$x^2 + (3 - \lambda)x + 2 = \lambda$
has the least value, is –
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Solution
The number of integral values of $k$ for which one root of the equation $2x^{2}-8x+k=0$ lies in the interval $(1,2)$ and its other root lies in the interval $(2,3)$ is:
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Solution
Let $\alpha$ and $\beta$ be the roots of equation $px^{2}+qx+r=0$, $p\ne 0$.
If $p,q,r$ are in A.P. and $\dfrac{1}{\alpha}+\dfrac{1}{\beta}=4$, then the
value of $|\alpha-\beta|$ is :
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Solution
If $\alpha $ and $\beta $ are the roots of the equation2x(2x + 1) = 1, then $\beta $ is equal to :
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Solution
If $\lambda \in \mathbb{R}$ is such that the sum of the cubes of the roots of the equation $x^{2} + (2-\lambda)x + (10-\lambda)=0$ is minimum, then the magnitude of the difference of the roots of this equation is :
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Solution
If one real root of the quadratic equation $81x^{2}+kx+256=0$ is cube of the other root, then a value of $k$ is :
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Solution
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