Let \( S \) be the set of all non-zero real numbers \( \alpha \) such that the quadratic equatio... VIDEO
Let \( S \) be the set of all non-zero real numbers \( \alpha \) such that the quadratic equation \( \alpha x^{2}-x+\alpha=0 \) has two distinct real roots \( x_{1} \) and \( x_{2} \) satisfying the inequality \( \left|x_{1}-x_{2}\right|2 \).https://bit.ly/YTAI_PWAP https://www.pw.live
Other Videos By PW Solutions 2023-07-03 Consider the following statements:
\( S_{1} \) : If the roots of \( x^{2}-b x+c=0 \) are two con... 2023-07-03 Number of solutions of the equation
\( \sqrt{3 x-2}+\sqrt{4 x+4}=\sqrt{5 x+1}+\sqrt{4 x-5} \) is... 2023-07-03 The equation \( 2^{2 x}+(a-1) 2^{x+1}+a=0 \) has roots of opposite signs then exhaustive set of ... 2023-07-03 Values of \( \mathrm{k} \) for which the inequality \( k \sin ^{2} x-k \sin x+1 \geq 0 \) is tru... 2023-07-03 The values of \( a \) and \( b \) so that \( x^{4}+12 x^{3}+46 x^{2}+a x+b \) is square of quadr... 2023-07-03 For the equation
\( \sqrt[3]{(a+x)^{2}}+4 \sqrt[3]{(a-x)^{2}}=5 \sqrt[3]{a^{2}-x^{2}} \) incorre... 2023-07-03 If the roots of the equation \( a x^{2}-b x+c=0 \) are \( \alpha, \beta \), then the roots of th... 2023-07-03 If \( a, b, c \in R, a \neq 0 \) and \( (b-1)^{2}4 a c \), then the number of real roots of the ... 2023-07-03 Polynomials \( f(x) \) and \( g(x) \) are defined as follows:
\[
f(x)=x^{2}+a x+2 ; g(x)=x^{2}+2... 2023-07-03 If \( r, s, t \) and \( u \) are roots of \( x^{4}-5 x+3=0 \), then for the equation whose roots... 2023-07-03 Let \( S \) be the set of all non-zero real numbers \( \alpha \) such that the quadratic equatio... 2023-07-03 The set of values of \( K(K \in R) \) for which the equation \( x^{2}-4 \) \( |x|+3-\left|K^{2}-... 2023-07-03 Let \( \alpha \) and \( \beta \) be the roots of \( x^{2}-6 x-2=0 \), with \( \alpha\beta \). If... 2023-07-03 \[
A=\left\{x: \frac{x+2}{x-4} \leq 0\right\}, B=\left\{x / x^{2}-a x-4 \leq 0\right\}
\]
If \( ... 2023-07-03 The number of real roots of equation \( x^{8}-x^{5}+x^{2}-x+2= \) 0 is (a) 2 (b) 4 (c) 6 (d) 0 2023-07-03 A value of \( b \) for which the equations
\[
\begin{array}{l}
x^{2}+b x-1=0 \\
x^{2}+x+b=0
\end... 2023-07-03 Let \( p \) and \( q \) be real numbers such that \( p=0, p^{3}=q \) and \( p^{3} \) \( =-q \). ... 2023-07-03 Let \( \left(x_{0}, y_{0}\right) \) be the solution of the following equations \( (2 x)^{\ln 2}=... 2023-07-03 Let \( \alpha, \beta \) be the roots of the equation \( x^{2}-p x+r=0 \) and \( \frac{\alpha}{2}... 2023-07-03 Let \( a, b, c \) be the sides of a triangle where \( a \neq b \neq c \) and \( \lambda \in R \)... 2023-07-03 Let \( f(x) \) be the remainder when \( p(x)=x^{73}-2 x^{6}+3 x^{3} \) is divided by \( x^{4}\le...
0