JEE Advanced · 2022 · 28 Aug 2022 · Paper 2 · Quadratic Equations and Inequalities

More JEE Advanced questions on Quadratic Equations and Inequalities

1. Match each entry in List-I to the correct entry in List-II and choose the correct option.
   

   List-I	List-II

   | (P) If $\alpha$ and $\beta$ are the distinct roots of the equation ${\mathrm{x}}^2+\mathrm{x}+1=0$, then the quadratic equation with roots …
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2. Let a,b,c be positive integers in arithmetic progression such that the equation
   ${\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}=0$
   has only integer solutions.
   Then which of the following statements is (are) TRUE ?
   (A) $\mathrm{c}-\mathrm{b}$ is an integer multiple of a
   (B) Both the roots …
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3. Let ${\mathbb{R}}^2$ denote $\mathbb{R}\times \mathbb{R}$. Let
   $\mathrm{S}=\{(\mathrm{a},\mathrm{b},\mathrm{c}):\mathrm{a},\mathrm{b},\mathrm{c}\in \mathbb{R}$ and ${\mathrm{ax}}^2+2\mathrm{bxy}+{\mathrm{cy}}^2>0$ for all …
   JEE Advanced 2024 Copy linkView solution →
4. Let $f(\mathrm{x})={\mathrm{x}}^4+{\mathrm{ax}}^3+{\mathrm{bx}}^2+\mathrm{c}$ be a polynomial with real coefficients such that $f(1)=-9$. Suppose that $\mathrm{i}\sqrt{3}$ is a root of the equation $4{\mathrm{x}}^3+3{\mathrm{ax}}^2+2\mathrm{bx}=0$, where …
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5. For $x\in \mathbb{R}$, the number of real roots of the equation $3x^2-4|x^2-1|+x-1=0$ is ____.
   JEE Advanced 2021 Copy linkView solution →
6. Suppose a, b denote the distinct real roots of the quadratic polynomial $x^2+20x-2020$ and suppose c, d denote the distinct complex roots of the quadratic polynomial $x^2-20x+2020$. Then the value of
   

   $$ac(a-c)+ad(a-d)+bc(b-c)+bd(b-d)$$

   
   is
   JEE Advanced 2020 Copy linkView solution →