COMEDK · Maths · 2. Quadratic Equation
The number of solutions for the equation \(x^{2}-5|x|+6=0\) is
- A \(4\)
- B \(3\)
- C \(2\)
- D \(1\)
Answer & Solution
Correct Answer
(A) \(4\)
Step-by-step Solution
Detailed explanation
We have, \[ \begin{aligned} x^{2}-5|x|+6 &=0 \\ |x|^{2}-5|x|+6 &=0 \\ (|x|-3)(|x|-2) &=0 \\ |x| &=3,2 \\ \Rightarrow \quad \quad x &=\pm 3, \pm 2 \\ \therefore & \text { Number of solution is } 4 . \end{aligned} \]
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
- Let point Q be the image of point \(P(2, -1)\) in the line \(3x + 5 = 4y\). Find the area of the circle that has the segment PQ as the diameter.COMEDK 2026 Medium
- If the foci of the ellipse \(\frac{x^{2}}{25}+\frac{y^{2}}{b^{2}}=1\) and the hyperbola \(\frac{x^{2}}{144}-\frac{y^{2}}{81}=\frac{1}{25}\) coincide, then the value of \(b^{2}\) isCOMEDK 2018 Easy
- \(\int_{-\pi / 2}^{\pi / 2} \sin x d x\)COMEDK 2021 Easy
- If \(\lim _{x \rightarrow \infty}\left(1+\dfrac{a}{x}+\dfrac{b}{x^2}\right)^{2 x}=e^2\), thenCOMEDK 2022 Hard
- If a circle with the point \((-1,1)\) as its center touches the straight line \(x+2 y+9=0\), then the coordinates of the points of contact isCOMEDK 2018 Easy
- \(\int\limits_{-\pi / 2}^{\pi / 2} \sin ^2 x d x\) is equal toCOMEDK 2023 Easy
More PYQs from COMEDK
- If \(\omega\) is a cube root of unity, then the value of \(\operatorname{determinant}\left|\begin{array}{ccc}1+\omega & \omega^{2} & \omega \\ \omega^{2}+\omega & -\omega & \omega^{2} \\ 1+\omega^{2} & \omega & \omega^{2}\end{array}\right|\) is equal toCOMEDK 2012 Easy
- A block of wood floats in water with \((4 / 5)\) th of its volume submerged. If the same block just floats in a liquid, the density of the liquid is (in \(\mathrm{kgm}^{-3}\))COMEDK 2023 Easy
- The ratio of minimum wavelength of Lyman and Balmer series will beCOMEDK 2018 Easy
- \(\text { If } f(x)=\sin ^{-1}\left(\dfrac{2^{x+1}}{1+4^x}\right) \text { then } f^{\prime}(0) \text { is equal to }\)COMEDK 2023 Medium
- Ozone in stratosphere is depleted byCOMEDK 2023 Easy
- Identify the organic compound which, on heating with strong solution of \(\mathrm{NaOH}\), partly converted into an acid salt and partly into alcoholCOMEDK 2013 Medium