WebIf the roots of the equation px 2+2qx+r=0 and qx 2−2 prx+q=0 be real, then A p=q B q 2=pr C p 2=qr D r 2=pq Medium Solution Verified by Toppr Correct option is B) Equation px … Web13 jan. 2024 · Explanation: As px2 + qx +r = 0 and qx2 + rx + p = 0 have common root, let this root be α. Then pα2 +qα +r = 0 and qα2 + rα + p = 0 and hence α2 pq −r2 = α qr − p2 = 1 pr − q2 and α = qr −p2 pr − q2 and α2 = pq −r2 pr −q2 i.e. (qr −p2)2 (pr −q2)2 = pq −r2 pr −q2 or (qr −p2)2 = (pq− r2)(pr −q2) or q2r2 +p4 − 2p2qr = p2qr −pq3 −pr3 + q2r2

If the roots of the equation px^2 + 2qx + r = 0 and qx^2 - 2√(pr)x …

Web2 jan. 2015 · Here is the question: If the roots of the equation $$ x^4 - px^3 + qx^2 - pqx + 1 = 0 $$ are $\alpha, \beta, \gamma,$ and $\delta$, show that $$ (\alpha + \beta ... Web19 nov. 2024 · selected Nov 21, 2024 by SumanMandal Best answer Let , a/R, a, aR be the roots of x3 – px2 + qx – r = 0 Then product of the roots = a/R .a. aR = a3 = r ⇒ a = r1/3 … how to wire a dayton electric motor

Solve x^3+px+q=0 Microsoft Math Solver

WebStep 1: Find the third root. For the cubic equation x 3 + p x 2 - q x + r = 0, the sum of the three roots is - p. But it is given that the sum of the two roots is 0. So the third root is - … Web31 mrt. 2024 · If α, β, γ are the roots of the equation x 3 + px 2 + qx + r = 0, then α 2 β 2 + α 2 γ 2 + β 2 γ 2 is equal to This question was previously asked in UP TGT Mathematics … Web14 okt. 2005 · If the roots of the equation x^3 + px^2 + qx + r=0 form consecutive terms of a geometric sequence, prove that q^3=p^3r. Show that this condition is satisfied for the … origin of lotha naga