JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
The sum of the real roots of the equation \(\left| {\begin{array}{*{20}{c}}
x&{ - 6}&{ - 1}\\
2&{ - 3x}&{x - 3}\\
{ - 3}&{2x}&{x = 2}
\end{array}} \right| = 0\) is equal to
- A \(-4\)
- B \(0\)
- C \(6\)
- D \(1\)
Answer & Solution
Correct Answer
(B) \(0\)
Step-by-step Solution
Detailed explanation
By expansion, we get \( - 5{x^3} + 30x - 30 + 5x = 0\) \( \Rightarrow - 5{x^3} + 35x - 30 = 0\) \( \Rightarrow {x^3} - 7x + 6 = 0\), All roots srea real So, sum of roots \(=0\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- Each of the angles \(\beta\) and \(\gamma\) that a given line makes with the positive y - and z -axes, respectively, is half of the angle that this line makes with the positive x -axes. Then the sum of all possible values of the angle \(\beta\) isJEE Mains 2025 Medium
- The shortest distance between the lines \(\frac{x-4}{4}=\frac{y+2}{5}=\frac{z+3}{3}\) and \(\frac{x-1}{3}=\frac{y-3}{4}=\frac{z-4}{2}\) isJEE Mains 2023 Medium
- The sum of coefficients of integral power of \(x\) in the binomial expansion \({\left( {1 - 2\sqrt x } \right)^{50}}\) is :JEE Mains 2015 Hard
- The number of terms of an A.P. is even; the sum of all the odd terms is 24 , the sum of all the even terms is 30 and the last term exceeds the first by \(\frac{21}{2}\). Then the number of terms which are integers in the A.P. is :JEE Mains 2025 Medium
- Let \(f\) and \(g\) be continuous functions on \([0, a]\) such that \(f(x) = f(a -x)\) and \(g(x) + g(a -x) = 4\), then \(\int\limits_0^a {f\left( x \right)g\left( x \right)dx} \) is equal toJEE Mains 2019 Hard
- The mean age of \(25\) teachers in a school is \(40\, years\). A teacher retires at the age of \(60\, years\) and a new teacher is appointed in his place. If now the mean age of the teachers in this school is \(39\, years\), then the age (in years) of the newly appointed teacher isJEE Mains 2017 Medium
More PYQs from JEE Mains
- Let \(P(3,2,3), Q(4,6,2)\) and \(R(7,3,2)\) be the vertices of \(\triangle \mathrm{PQR}\). Then, the angle \(\angle \mathrm{QPR}\) isJEE Mains 2024 Hard
- Let the line \(x=-1\) divide the area of the region \(\{(x,y):1+x^{2}\le y\le3-x\}\) in the ratio \(m:n\), \(\gcd(m,n)=1\). Then \(m+n\) is equal toJEE Mains 2026 Easy
- If the function \(f(x)=\left\{\begin{array}{cc}\frac{72^x-9^x-8^x+1}{\sqrt{2}-\sqrt{1+\cos x}} & , x \neq 0 \\ a \log _e 2 \log _e 3 & , x=0\end{array}\right.\) is continuous at \(x=0\), then the value of \(a^2\) is equal toJEE Mains 2024 Hard
- Let \(A=\left(\begin{array}{rrr}1 & -1 & 0 \\ 0 & 1 & -1 \\ 0 & 0 & 1\end{array}\right)\) and \(B=7 A^{20}-20 A^{7}+2 I\), where \(I\) is an identity matrix of order \(3 \times 3\) If \(B=\left[b_{i j}\right]\), then \(b_{13}\) is equal to \(....\)JEE Mains 2021 Hard
- If \(a+\alpha=1, b+\beta=2\) and \(\operatorname{af}(x)+\alpha f\left(\frac{1}{x}\right)=b x+\frac{\beta}{x}, x \neq 0,\) then the value of expression \(\frac{ f ( x )+ f \left(\frac{1}{ x }\right)}{ x +\frac{1}{ x }}\) is ..... .JEE Mains 2021 Hard
- If \(\alpha > \beta > 0\) are the roots of the equation \(ax ^2+ bx +\) \(1=0\), and \(\lim _{x \rightarrow \frac{1}{\alpha}}\left(\frac{1-\cos \left(x^2+b x+a\right)}{2(1-\alpha x)^2}\right)^{\frac{1}{2}}=\frac{1}{k}\left(\frac{1}{\beta}-\frac{1}{\alpha}\right)\), then \(k\) is equal toJEE Mains 2023 Hard