AP EAMCET · Maths · Quadratic Equation
The number of solutions of the equation \(\sqrt{3 x^2+x+5}=x-3\) is
- A \(2\)
- B \(1\)
- C \(0\)
- D \(4\)
Answer & Solution
Correct Answer
(C) \(0\)
Step-by-step Solution
Detailed explanation
Domain: \(x-3 \ge 0 \implies x \ge 3\) \(3 x^2+x+5=(x-3)^2\) \(3 x^2+x+5=x^2-6x+9\) \(2x^2+7x-4=0\) \(x=\frac{-7 \pm \sqrt{7^2-4(2)(-4)}}{2(2)}\) \(x=\frac{-7 \pm \sqrt{49+32}}{4}\) \(x=\frac{-7 \pm 9}{4}\) \(x_1=\frac{2}{4}=\frac{1}{2}\) \(x_2=\frac{-16}{4}=-4\) Check solutions…
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
- If the function \(f(x)=\sin x-\cos ^2 x\) is defined on the interval \([-\pi, \pi]\), then \(f\) is strictly increasing in the intervalAP EAMCET 2025 Medium
- If is a tangent drawn to the curve at where are constants, thenAP EAMCET 2019 Easy
- \(\lim _{n \rightarrow \infty} \frac{1}{n^3} \sum_{k=1}^n k^2 x=\)AP EAMCET 2025 Medium
- If \(S=\left[\begin{array}{lll}0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0\end{array}\right]\) and \(A=\frac{1}{2}\left[\begin{array}{lll}b+c & c-a & b-a \\ c-b & c+a & a-b \\ b-c & a-c & a+b\end{array}\right]\), then \(\mathrm{SAS}^{-1}=\)AP EAMCET 2023 Easy
- The vector \(\mathbf{c} .(\mathbf{b}+\mathbf{c}) \times(\mathbf{a}+\mathbf{b}+\mathbf{c})\) is equal toAP EAMCET 2004 Easy
- If then the value of
AP EAMCET 2020 Medium
More PYQs from AP EAMCET
- The least intercept made by a tangent to the ellipse \(\frac{x^2}{64}+\frac{y^2}{49}=1\) with coordinate axes isAP EAMCET 2022 Hard
- The value of \(\lim _{\substack{n \rightarrow \infty}} \frac{1}{n^3} \sum_{k=1}^n\left(k^2 x\right)\) isAP EAMCET 2004 Hard
- If A \((1,0,2), \mathrm{B}(2,1,0), \mathrm{C}(2,-5,3), \mathrm{D}(0,3,2)\) are four points and the point of intersection of the lines AB and CD is \(\mathrm{P}(a, b, c)\), then \(a+b+c=\)AP EAMCET 2024 Medium
- Let \(A=\left[\begin{array}{cc}2 & -5 \\ 3 & 1\end{array}\right]\), what is \(f(A)=\) ?, where \(f(x)=x^3-2 x^2-5\).AP EAMCET 2021 Hard
- The hybridizations of carbon in graphite, diamond and are respectivelyAP EAMCET 2022 Easy
- In the given reaction sequence conversion of Y to Z is
AP EAMCET 2025 Medium