JEEAdvanced
The cubic x^3 - a x^2 + (a - 1)x - 5 = 0 (with a a real parameter)…
Question
The cubic x^3 - a x^2 + (a - 1)x - 5 = 0 (with a a real parameter) has roots whose squares sum to 10. Determine the largest possible value of a.
✓ Verified answer: 4checked by our engine — not a guess
Step-by-step solution
Let the roots be r,s,t. Vieta gives r+s+t = a and rs+rt+st = a - 1. Then
r^2+s^2+t^2 = (r+s+t)^2 - 2(rs+rt+st) = a^2 - 2(a-1) = a^2 - 2a + 2.
Set this equal to 10: a^2 - 2a + 2 = 10, i.e. a^2 - 2a - 8 = 0, giving (a-4)(a+2)=0, so a = 4 or a = -2.
The largest value is a = 4.
Final answer4
Stuck on a problem like this?
Paste any JEE or NEET question — verified working, a confidence %, and an honest “not sure” instead of a bluff.
Solve my doubt →More Algebra solutions
Let a, b, c be the (possibly complex) roots of the cubic x^3 - 5x^2 +…JEE · MathA function f defined for all nonzero real x satisfies f(x) + 2 f(1/x)…JEE · MathLet a, b, c be positive real numbers with abc = 8. Find the minimum…JEE · MathA polynomial P(x) leaves remainder 3 on division by (x - 1),…JEE · MathLet w be the real number w = cbrt(20 + 14√2) + cbrt(20 - 14√2), where…JEE · MathEvaluate the sum S = 1·1! + 2·2! + 3·3! + 4·4! + 5·5! + 6·6!, where…JEE · MathReal numbers a, b, c satisfy a + b + c = 6, a^2 + b^2 + c^2 = 14, and…JEE · MathFind the greatest integer not exceeding (2 + √5)^5; that is, compute…JEE · Math