(B) Given the equation: $x(x + 2) = 3 - ax^2$ Rearranging the terms: $x^2 + 2x = 3 - ax^2$ $(1 + a)x^2 + 2x - 3 = 0$ For a quadratic equation $Ax^2 +

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(B) Given the equation: $x(x + 2) = 3 - ax^2$ Rearranging the terms: $x^2 + 2x = 3 - ax^2$ $(1 + a)x^2 + 2x - 3 = 0$ For a quadratic equation $Ax^2 + Bx + C = 0$ to have one root approaching infinity,the coefficient of the highest degree term must approach zero. Therefore,$1 + a \to 0$ $a \to -1$

Class 11 Mathematics 4-2.Quadratic Equations and Inequations Solution of quadratic equations and Nature of roots

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If one root of the equation $x(x + 2) = 3 - ax^2$ approaches infinity,then the value of $a$ approaches which of the following?

A
$1$
B
$-1$
C
$2$
D
$4$

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4-2.Quadratic Equations and Inequations

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Solution of quadratic equations and Nature of roots

The sum of all real values of $x$ satisfying the equation $(x^2 - 5x + 5)^{x^2 + 4x - 60} = 1$ is:

DifficultJEE MAIN 2016

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Let $f(x)$ be a quadratic expression such that $f(0)+f(1)=0$. If $f(-2)=0$,then

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If $\alpha, \beta, \gamma$ are roots of $x^3 + x^2 - 5x - 1 = 0$,then the value of $[\alpha] + [\beta] + [\gamma]$ is (where $[.]$ denotes the greatest integer function):

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Let $\alpha$ and $\beta$ be the roots of the equation $(x - a)(x - b) = c$,where $c \neq 0$. What are the roots of the equation $(x - \alpha)(x - \beta) + c = 0$?

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If the roots of the equations $px^2 + 2qx + r = 0$ and $qx^2 - 2\sqrt{pr}x + q = 0$ are real,then .........

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If one root of the equation $x(x + 2) = 3 - ax^2$ approaches infinity,then the value of $a$ approaches which of the following?

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The sum of all real values of $x$ satisfying the equation $(x^2 - 5x + 5)^{x^2 + 4x - 60} = 1$ is:

Let $f(x)$ be a quadratic expression such that $f(0)+f(1)=0$. If $f(-2)=0$,then

If $\alpha, \beta, \gamma$ are roots of $x^3 + x^2 - 5x - 1 = 0$,then the value of $[\alpha] + [\beta] + [\gamma]$ is (where $[.]$ denotes the greatest integer function):

Let $\alpha$ and $\beta$ be the roots of the equation $(x - a)(x - b) = c$,where $c \neq 0$. What are the roots of the equation $(x - \alpha)(x - \beta) + c = 0$?

If the roots of the equations $px^2 + 2qx + r = 0$ and $qx^2 - 2\sqrt{pr}x + q = 0$ are real,then .........

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