TS EAMCET · Maths · Quadratic Equation
If the harmonic mean between the roots of \((5+\sqrt{2}) x^2-b x+(8+2 \sqrt{5})=0\) is 4 , then the value of \(b\) is
- A \(2\)
- B \(3\)
- C \(4-\sqrt{5}\)
- D \(4+\sqrt{5}\)
Answer & Solution
Correct Answer
(D) \(4+\sqrt{5}\)
Step-by-step Solution
Detailed explanation
Given equation is \[ (5+\sqrt{2}) x^2-b x+(8+2 \sqrt{5})=0 \] Let \(\alpha\) and \(\beta\) be the roots of this equation. \[ \therefore \] \[ \begin{aligned} \alpha+\beta & =\frac{b}{5+\sqrt{2}} \\ \alpha \beta & =\frac{8+2 \sqrt{3}}{5+\sqrt{2}} \end{aligned} \] Given that…
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
- Suppose \(A\) and \(B\) are events of a random experiment such that \(P(A)=\frac{1}{3}, P(A \cap B)=\frac{1}{5}\) and \(P(A \cup B)=\frac{3}{5}\). Then, match the items of List-I with the items of List-II
TS EAMCET 2018 Medium - The function \(f: C \rightarrow C\) defined by \(f(x)=\frac{a x+d}{c x+d}\) for \(x \in C\) where \(b d \neq 0\) reduces to a constant function, ifTS EAMCET 2005 Easy
- \(\sinh { }^1 2+\cosh ^1 2-\tanh { }^1 \frac{2}{3}+\operatorname{coth}^1(-2)=\)TS EAMCET 2018 Medium
- If \(\frac{x+3}{(x+1)\left(x^2+2\right)}=\frac{a}{x+1}+\frac{b x+c}{x^2+2}\) then \(a-b+c=\)TS EAMCET 2025 Easy
- The equation represents a pair of lines for the ordered pairTS EAMCET 2022 Easy
- The value of the series \(\cos 12^{\circ}+\cos 84^{\circ}\) \(+\cos 132^{\circ}+\cos 156^{\circ}\) isTS EAMCET 2004 Easy
More PYQs from TS EAMCET
- The point \((4,1)\) undergoes the following transformations successively I. Reflection about the line \(y=x\) II. Translation through a distance 2 units in the direction of positive \(X\)-axis. III. Rotation through an angle \(\frac{\pi}{4}\) about origin in the anticlockwise direction. Then, the final position of the point isTS EAMCET 2018 Easy
- If the straight line \(y=m x+c\) is parallel to the axis of the parabola \(y^2=l x\) and intersects the parabola at \(\left(\frac{c^2}{8}, c\right)\), then the length of the latusrectum isTS EAMCET 2011 Easy
- If \(2 x^2-10 x y+2 \lambda y^2+5 x-16 y-3=0\) represents a pair of straight lines, then point of intersection of those lines isTS EAMCET 2017 Medium
- \(\int_0^{\pi / 4} \frac{1}{5 \cos ^2 x+16 \sin ^2 x+8 \sin x \cos x} d x=\)TS EAMCET 2025 Medium
- The product \(D\) in the following reaction sequence is
TS EAMCET 2020 Medium - If \(m\) and \(\mathrm{M}\) are respectively the smallest and greatest rational roots of the equation \(6 x^6-25 x^5+31 x^4-31 x^2+25 x-6=0\), then \(\mathrm{M}-m=\)TS EAMCET 2022 Easy