Let α be the minimum value of f(x)=5 x2-2 x+(26/5) and the graph of f(x) is symmetric about x =β. Also, S n =α+(α+β)+(α+2 β)+(α+3 β)+ ldots ldots ldots upto n terms. The value of α is equal to

Question

Let α be the minimum value of f(x)=5 x2-2 x+(26/5) and the graph of f(x) is symmetric about x =β. Also, S n =α+(α+β)+(α+2 β)+(α+3 β)+ ldots ldots ldots upto n terms. The value of α is equal to (A) -5 (B) 5 (C) (-5/2) (D) (5/2)

Tardigrade Admin · Accepted Answer

f(x)=5 x2-2 x+(26/5)=5(x-(1/5))2+5 ∴ f min (x=(1/5))=5 ≡ α

Q. Let $α$ be the minimum value of $f (x) = 5 x^{2} - 2 x + \frac{26}{5}$ and the graph of $f (x)$ is symmetric about $x = β$ . Also, $S_{n} = α + (α + β) + (α + 2 β) + (α + 3 β) + \dots\dots\dots$ upto $n$ terms.
The value of $α$ is equal to

-5

5

$\frac{- 5}{2}$

$\frac{5}{2}$

$f (x) = 5 x^{2} - 2 x + \frac{26}{5} = 5 (x - \frac{1}{5})^{2} + 5$
$∴ f_{m i n} (x = \frac{1}{5}) = 5 \equiv α$

Q. Let α be the minimum value of f(x)=5x2−2x+526​ and the graph of f(x) is symmetric about x=β. Also, Sn​=α+(α+β)+(α+2β)+(α+3β)+……… upto n terms. The value of α is equal to

-5

5

2−5​

25​

f(x)=5x2−2x+526​=5(x−51​)2+5 ∴fmin​(x=51​)=5≡α

Q. Let $α$ be the minimum value of $f (x) = 5 x^{2} - 2 x + \frac{26}{5}$ and the graph of $f (x)$ is symmetric about $x = β$ . Also, $S_{n} = α + (α + β) + (α + 2 β) + (α + 3 β) + \dots\dots\dots$ upto $n$ terms.
The value of $α$ is equal to

$\frac{- 5}{2}$

$\frac{5}{2}$

$f (x) = 5 x^{2} - 2 x + \frac{26}{5} = 5 (x - \frac{1}{5})^{2} + 5$
$∴ f_{m i n} (x = \frac{1}{5}) = 5 \equiv α$