Let \( a, b \in \mathrm{R} \) be such that the equation \( a x^{2}-2 b x+15=0 \) has a repeated ... VIDEO
Let \( a, b \in \mathrm{R} \) be such that the equation \( a x^{2}-2 b x+15=0 \) has a repeated root \( \alpha \). If \( \alpha \) and \( \beta \) are the roots of the equation \( x^{2}-2 b x+21=0 \), then \( \alpha^{2}+\beta^{2} \) is equal to:
(a) 37
(b) 58
(c) 68
(d) 92
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live
Other Videos By PW Solutions 2023-07-03 If one root of the equation \( a x^{2}+b x+c=0 \) is equal to \( n^{\text {th }} \) power of the... 2023-07-03 If \( (2+i)(2+2 i)(2+3 i) \ldots(2+n i)=x+i y \), then the value of 5.8.13... \( \left(4+n^{2}\r... 2023-07-03 The complex number \( \omega \) satisfying the equation \( \omega^{3}=8 \mathrm{i} \) and lying ... 2023-07-03 The equation \( x^{\frac{3}{4}\left(\log _{2} x\right)^{2}+\log _{2} x-\frac{5}{4}}=\sqrt{2} \) ... 2023-07-03 Which of the following is equal to \( \sqrt[3]{-1} \) ?
(a) \( \frac{\sqrt{3}+\sqrt{-1}}{2} \)
(... 2023-07-03 If \( |z-\mathrm{i} \operatorname{Re}(z)|=|z-\operatorname{lm}(z)| \), then
(a) \( \operatorname... 2023-07-03 If \( |z-i| \leq 2 \) and \( z_{0}=5+3 i \) then the maximum value of \( \mid i z \) \( +z_{0} \... 2023-07-03 If the sum of all the roots of the equation \( e^{2 x}-11 e^{x}-45 e^{-x}+ \) \( \frac{81}{2}=0 ... 2023-07-03 The largest interval for which \( x^{12}-x^{9}+x^{4}-x+10 \) is
(a) \( -4x \leq 0 \)
(b) \( 0x1 ... 2023-07-03 Let \( \alpha, \beta \) be the roots of the equation \( x^{2}-4 \lambda x+5=0 \) and \( \alpha \... 2023-07-03 Let \( a, b \in \mathrm{R} \) be such that the equation \( a x^{2}-2 b x+15=0 \) has a repeated ... 2023-07-03 Let \( \mathrm{p} \& \mathrm{q} \) are real numbers such that \( (\tan p-1)^{3}+2019 \) \( (\tan... 2023-07-03 If the sum of the squares of the reciprocals of the roots \( \alpha \) and \( \beta \) of the eq... 2023-07-03 If the quadratic equation \( x^{2}+(2-\tan \theta) x-(1+\tan \theta)=0 \) has two integral roots... 2023-07-03 If \( a, b, c \), be the roots of the equation \( x^{3}+m x+n=0 \), then
\[
\frac{6\left(a^{5}+b... 2023-07-03 If \( a+b+c=0, a^{2}+b^{2}+c^{2}=4 \), then \( a^{4}+b^{4}+c^{4} \) 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... 2023-07-03 If the fraction \( \frac{x^{3}+(a-10) x^{2}-x+a-6}{x^{3}+(a-6) x^{2}-x+a-10} \) reduces to quoti... 2023-07-03 If the cubic \( 2 x^{3}-9 x^{2}+12 x+k=0 \) has two equal roots then maximum value of \( |k| \) is 2023-07-03 If \( a, b \in R \) such that \( a+b=1 \) and \( (1-2 a b)\left(a^{3}+\mathrm{b}^{3}\right)=12 \... 2023-07-03 If \( a, b, c \) are non-zero real number, then the minimum value of the expression
\[
\left(\fr...