AP EAMCET · Maths · Quadratic Equation
If \(a, b\) and \(c\) are the roots of \(x^3+4 x+1=0\), then \(\frac{1}{a+b}+\frac{1}{b+c}+\frac{1}{c+a}=\)
- A 2
- B 3
- C 4
- D -4
Answer & Solution
Correct Answer
(C) 4
Step-by-step Solution
Detailed explanation
\(a, b, c\) are roots of \(x^3+4 x+1=0\) \[ \begin{aligned} \Rightarrow & x^3+0 \cdot x^2+4 x+1=0 \\ \text { So, } & a+b+c=0 \Rightarrow a b c=-1 \end{aligned} \] \[ \text { and } a b+b c+c a=4 \] Now,…
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 and , thenAP EAMCET 2022 Medium
- If \(x^2+y^2=25\), then \(\log _5[\max (3 x+4 y)]\) isAP EAMCET 2015 Hard
- In a \(\triangle A B C\), the correct formulae among the following areAP EAMCET 2004 Hard
- If \(\alpha, \beta, \gamma\) are any three angles, then \(\cos \alpha+\cos \beta-\cos \gamma-\cos (\alpha+\beta+\gamma)=\)AP EAMCET 2018 Medium
- If \(A\) and \(B\) are the two real values of \(k\) for which the system of equations \(x+2 y+z=1\), \(x+3 y+4 z=k \cdot x+5 y+10 z=k^2\) is consistent, then \(A+B=\)AP EAMCET 2018 Medium
- If \(a, b\) and \(c\) are the roots of \(x^3+q x+r=0\), then \((a-b)^2+(b-c)^2+(c-a)^2=\)AP EAMCET 2018 Medium
More PYQs from AP EAMCET
- The equation of the circle which cuts the circles
\(\begin{aligned}
& S_1 \equiv x^2+y^2-4=0 \\
& S_2 \equiv x^2+y^2-6 x-8 y+10=0 \\
& S_3 \equiv x^2+y^2+2 x-4 y-2=0
\end{aligned}\)
at the extremities of diameters of these circles isAP EAMCET 2019 Easy - An earthquake generates both transverse \(S\) and longitudinal \(P\) waves in the earth with speeds \(4.5 \mathrm{~km} \mathrm{~s}^{-1}\) and \(8.0 \mathrm{~km} \mathrm{~s}^{-1}\), respectively. A seismograph records that the first \(P\)-wave arrives 3.5 minutes earlier than the first S-wave. From the seismograph, the epicentre of the earthquake is located at a distance.AP EAMCET 2019 Hard
- A problem in Algebra is given to two students \(A\) and \(B\) whose chances of solving it are \(\frac{2}{5}\) and \(\frac{3}{4}\) respectively. The probability that the problem is solved if both of them try independently isAP EAMCET 2025 Medium
- If the foot of the perpendicular from \((0,0,0)\) to a plane is \((1,2,3)\), then the equation of the plane isAP EAMCET 2012 Medium
- What is the volume (in litres) of oxygen required at STP to completely convert \(1.5 \mathrm{~mol}\) of sulphur into sulphur dioxide?AP EAMCET 2003 Easy
- The value of the determinant \(\left|\begin{array}{lll}b^2-a b & b-c & b c-a c \\ a b-a^2 & a-b & b^2-a b \\ b c-a c & c-a & a b-a^2\end{array}\right|\) isAP EAMCET 2015 Easy