WBJEE · Maths · Quadratic Equation
The roots of the quadratic equation \(x^2-2 \sqrt{3} x-22=0\) are :
- A imaginry
- B real, rational and equal
- C real, irrational and unequal
- D real, rational and unequal
Answer & Solution
Correct Answer
(C) real, irrational and unequal
Step-by-step Solution
Detailed explanation
\[ \text { Hints: } \begin{aligned} & x^2-2 \sqrt{3}-22=0 \\ & D=12+(4 \times 22)>0 \end{aligned} \] \(\because\) coeffs are irrational, \[ x=\frac{2 \sqrt{3} \pm \sqrt{12+88}}{2} \] \(\therefore\) Roots are irrational, real, unequal.
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
- Consider a tangent to the ellipse \(\frac{x^{2}}{2}+\frac{y^{2}}{1}=1\) at any point. The locus of the midpoint of the portion intercepted between the axes isWBJEE 2020 Medium
- If \(f(x)=2^{100} x+1, g(x)=3^{100} x+1\), then the set of real numbers \(x\) such that \(f[g(x)\}=x\) isWBJEE 2013 Easy
- The value of \(\sum_{r=2}^{\infty} \frac{1+2+\quad+(r-1)}{r !}\)WBJEE 2012 Hard
- Let \(f(x)>0\) for all \(x\) and \(f^{\prime}(x)\) exists for all \(x\). If \(f\) is the inverse function of \(h\) and \(h^{\prime}(x)=\frac{1}{1+\log x} \cdot\) Then, \(f^{\prime}(x)\) will beWBJEE 2019 Medium
- Consider the function \(f(x)=\frac{x^{3}}{4}-\sin \pi x+3\)WBJEE 2019 Medium
- A line passes through the point \((-1,1)\) and makes an angle \(\sin ^{-1}\left(\frac{3}{5}\right)\) in the positive direction of \(x\)-axis. If this line meets the curve \(x^2=4 y-9\) at \(A\) and \(B\), then \(|A B|\) is equal toWBJEE 2022 Easy
More PYQs from WBJEE
- The Entropy (S) of a black hole can be written as \(S=\beta k_B A\), where \(k_B\) is the Boltzmann constant and \(A\) is the area of the black hole. Then \(\beta\) has dimension ofWBJEE 2022 Medium
- In aqueous solution glucose remains asWBJEE 2011 Hard
- The value of the integral \(\int_{-1}^{1}\left\{\frac{x^{2013}}{e^{|x|}\left(x^{2}+\cos x\right)}+\frac{1}{e^{|x|}}\right\} d x\) is equal toWBJEE 2013 Easy
- The following figure shows the variation of potential energy V(x) of a particle with distance x. The particle has
WBJEE 2024 Easy - On the set \(R\) of real numbers, the relation \(\rho\) is defined by \(x \rho y,(x, y) \in R\)WBJEE 2018 Easy
- \(B\) is an extremity of the minor axis of an ellipse whose foci are \(S\) and \(S^{\prime} .\) If \(\angle S B S^{\prime}\) is a right angle, then the eccentricity of the ellipse isWBJEE 2017 Medium