AP EAMCET · Maths · Quadratic Equation
If the sum of two of the roots of \(x^3+p x^2-q x+r=0\) is zero, then \(p q\) is equal to
- A \(-r\)
- B \(r\)
- C \(2 r\)
- D \(-2 r\)
Answer & Solution
Correct Answer
(A) \(-r\)
Step-by-step Solution
Detailed explanation
Given that, \(x^3+p x^2-q x+r=0\) \(\ldots\) (i) Let \(\alpha, \beta, \gamma\) are roots of this equation \(\alpha+\beta+\gamma=-p\) \(\ldots\) (ii) \(\alpha \beta+\beta \gamma+\gamma \alpha=-q…
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 \(x-y+1=0\) meets the circle \(x^2+y^2+y-1=0\) at \(A\) and \(B\), then the equation of the circle with \(A B\) as diameter isAP EAMCET 2005 Medium
- If then equalsAP EAMCET 2022 Hard
- Let \(f(x)=x^2+a x+b\), where \(a, b \in R\). If \(f(x)=0\) has all its roots imaginary, then the roots of \(f(x)+f^{\prime}(x)+f^{\prime \prime}(x)=0\) areAP EAMCET 2009 Easy
- \(p_1\) and \(p_2\) are the perpendicular distances from the origin to the tangent and normal drawn at any point on the curve \(x^{2 / 3}+y^{2 / 3}=a^{2 / 3}\) respectively. If \(k_1 p_1^2+k_2 p_2^2=a^2\), then \(k_1+k_2=\)AP EAMCET 2024 Medium
- If the lines \(2 x+y+12=0, k x-3 y-10=0\) are conjugate with respect to the circle \(x^2+y^2-4 x+3 y-1=0\), then \(k=\)AP EAMCET 2018 Hard
- The equation of a curve passing through the point \((0,1)\), given that the slope of the tangent to the curve at any point \((x, y)\) is equal to the sum of the \(x\)-coordinate and the product of \(x\) and \(y\) coordinates at that point, isAP EAMCET 2021 Medium
More PYQs from AP EAMCET
- The number of ways of distributing 3 dozen fruits (no two fruits are identical) to 9 persons such that each gets the same number of fruits isAP EAMCET 2025 Medium
- At \(27^{\circ} \mathrm{C}\), two liquids A and B form an ideal solution with mole fractions 0.67 and 0.33 respectively. If the vapour pressure of pure \(A\) and \(B\) at \(27^{\circ} \mathrm{C}\) are \(300 \mathrm{~mm}\) and \(450 \mathrm{~mm}\) respectively, the total vapour pressure of the solution in \(\mathrm{mm}\) is:AP EAMCET 2017 Medium
- \(\begin{aligned} & \text { If } \cot \left(\cos ^{-1} x\right)=\sec \left\{\tan ^{-1}\left(\frac{a}{\sqrt{b^2-a^2}}\right)\right\}: \\ & b>a, \text { then } \mathrm{x}=\end{aligned}\)AP EAMCET 2017 Hard
- The equilibrium constant \(\left(K_C\right)\) for the following equilibrium
\(2 \mathrm{SO}_2(g)+\mathrm{O}_2(g) \rightleftharpoons 2 \mathrm{SO}_3(g)\)
at \(563 \mathrm{~K}\) is 100 . At equilibrium, the number of moles of \(\mathrm{SO}_3\) in the 10 litre flask is twice the number of moles of \(\mathrm{SO}_2\), then the number of moles of oxygen isAP EAMCET 2017 Medium - Identify the ortho and para directing groups towards aromatic electrophilic substitution reactions from the following list
I II III IV V VI AP EAMCET 2022 Medium - \(3 x+4 y-43=0\) is a tangent to the circle \(S \equiv x^2+y^2-6 x+8 y+k=0\) at a point P. If C is the centre of the circle and Q is a point which divides CP in the ratio \(-1: 2\), then the power of the point Q with respect to the circle \(\mathrm{S}=0\) isAP EAMCET 2025 Medium