TS EAMCET · Maths · Quadratic Equation
If the sum of two roots of the equation \(x^4-2 x^3+x^2+4 x-6=0\) is zero then the sum of the squares of the other two roots is
- A \(-6\)
- B \(1\)
- C \(-2\)
- D \(0\)
Answer & Solution
Correct Answer
(C) \(-2\)
Step-by-step Solution
Detailed explanation
\(r_1 + r_2 + r_3 + r_4 = 2\) Given \(r_1 + r_2 = 0 \implies r_3 + r_4 = 2\) \(r_1r_2r_3 + r_1r_2r_4 + r_1r_3r_4 + r_2r_3r_4 = -4\) Let \(r_1 = \alpha, r_2 = -\alpha\). Then \(\alpha(-\alpha)r_3 + \alpha(-\alpha)r_4 + \alpha r_3r_4 - \alpha r_3r_4 = -4\)…
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 \(\mathbf{P}, \mathbf{Q}, \mathbf{R}\) and \(\mathbf{S}\) are the points with position vectors \(\hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}, 2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+3 \hat{\mathbf{k}}, 2 \hat{\mathbf{i}}-3 \hat{\mathbf{k}}\) and \(3 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}+\hat{\mathbf{k}}\) respectively, then the angle between \(\mathbf{P Q}\) and \(\mathbf{R S}\) isTS EAMCET 2019 Easy
- In an isosceles right angled triangle, a straight line is drawn from the mid point of one of the equal sides to the opposite vertex. Then a pair of possible values of the cotangents of the two angles so formed at that vertex areTS EAMCET 2023 Medium
- If \(\int f(x) \cos x d x=\frac{1}{2}[f(x))^2+C\) and \(f(0)=0\), then \(f^{\prime}(0)=\)TS EAMCET 2017 Easy
- Let \(P\) be the point of intersection of the lines \(L_1 \equiv x-y-7=0\) and \(L_2 \equiv x+y-5=0\). \(A\left(x_1, y_1\right)\) and \(B\left(x_2, y_2\right)\) are points on the lines \(L_1=0\) and \(L_2=0\) respectively such that \(P A=3 \sqrt{2}, P B=\sqrt{2}, x_1, y_1 \geq 0, x_2, y_2 \geq 0\), then the angle made by the line segment \(A B\) at the origin isTS EAMCET 2020 Hard
- In a \(\triangle A B C, \sin A\) and \(\sin B\) satisfy \(c^2 x^2-c(a+b) x+a b=0\), thenTS EAMCET 2018 Medium
- If \(\cos \left(\frac{\pi}{4}-x\right) \cos 2 x+\sin x \sin 2 x \sec x\) \(=\cos x \sin 2 x \sec x+\cos \left(\frac{\pi}{4}+x\right) \cos 2 x\), then a possible value of sec \(x\) isTS EAMCET 2020 Medium
More PYQs from TS EAMCET
- A rod of length units slides with its ends on the coordinate axes. The locus of the midpoint of the rod isTS EAMCET 2021 Easy
- In uniform circular motion, which of the following statement is wrong?TS EAMCET 2021 Easy
- The power gain and voltage gain of a transistor connected in common emitter configuration are 1800 and 60 respectively. If the change in the emitter current is 0.62 mA, then the change in the collector current isTS EAMCET 2025 Medium
- The solution of the differential equation satisfying when , isTS EAMCET 2019 Easy
- If the product of the lengths of the perpendiculars drawn from the point \((-1,5)\) to the pair of lines \(2 x^2-x y+k y^2+6 x+y+4=0\) is \(\frac{65}{\sqrt{26}}\), then \(37 k^2+92 k\) is equal toTS EAMCET 2021 Easy
- At , the equilibrium constant of the process is . Standard free energy change (in ) of the process is approximatelyTS EAMCET 2018 Medium