Let f- R- R be the function fx - x - a1 x - a2 - x - a2 x - a3- x - x3x-x1 with a1- a 2- a3- R Then fx - 0 if and only if

You visited us 2 times! Enjoying our articles? Unlock Full Access!

Many One Function

Let f: R→ R...

Question

Let $f : R \to R$ be the function $f (x) = (x - a_{1}) (x - a_{2}) + (x - a_{2}) (x - a_{3}) + (x - x_{3}) (x - x_{1})$ with $a_{1}, a_{2}, a_{3} \in R$ Then f(x) $\geq 0$ if and only if

at least two of

a_{1}, a_{2}, a_{3}

are equal

No worries! We‘ve got your back. Try BYJU‘S free classes today!

a_{1} = a_{2} = a_{3}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

a_{1}, a_{2}, a_{3}

are all distinct

No worries! We‘ve got your back. Try BYJU‘S free classes today!

a_{1}, a_{2}, a_{3}

are all positive and3 distinct

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

Suggest Corrections

Similar questions

f : R \to R

f (x) = (x - a_{1}) (x - a_{2}) + (x - a_{2}) (x - a_{3}) + (x - a_{3}) (x - a_{1})

a_{1}, a_{2}, a_{3} \in R

f (x) \geq 0

a_{1}, a_{2}, a_{3}, . . . a_{n}

\frac{a_{1}}{a_{2} + a_{3} + . . . a_{n}}, \frac{a_{2}}{a_{1} + a_{3} + . . . a_{n}}, \frac{a_{3}}{a_{1} + a_{2} + a_{4} + . . . + a_{n}}, \frac{a_{n}}{a_{1} + a_{2} + . . . + a_{n}}

If A₁, A₂, A₃,..., A_n are n numbers between a and b, such that a, A₁, A₂, A₃,..., A_n, b are in A.P., then

a_{1}, a_{2}, a_{3} \in + R

\frac{a_{1}}{a_{2}} + \frac{a_{2}}{a_{3}} + \frac{a_{3}}{a_{1}} \geq 3

a_{1}, a_{2}, a_{3}, . . . . a_{n}

\frac{a_{1}}{a_{2} + a_{3} + . . . . + a_{n}}, \frac{a_{2}}{a_{1} + a_{3} + . . . . + a_{n}}, . . . ., \frac{a_{n}}{a_{1} + a_{2} + . . . . + a_{n - 1}}

Join BYJU'S Learning Program