The minimum value if the polynomial $p (x) = 3 x^{2} - 5 x + 2$ is

\frac{1}{6}

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

\frac{1}{12}

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

- \frac{1}{6}

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

- \frac{1}{12}

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

Open in App

Solution

The correct option is D $- \frac{1}{12}$
$p (x) = 3 x^{2} - 5 x + 2$

At maximum, $\frac{d}{d x} p (x) = p^{'} (x) = 0$

$⟹ 6 x - 5 = 0$

$⟹ x = \frac{5}{6}$

Hence maximum value of $p (x)$ is

$p (\frac{5}{6}) = 3 {(\frac{5}{6})}^{2} - 5 (\frac{5}{6}) + 2$

$= \frac{- 1}{12}$

Answer-(D)

Suggest Corrections

Similar questions

Statement1: The polynomial $P (x) = 4 x^{3} - 3 x^{2} + 5 x - 6$ when divided by $x - 1$ gives zero as the remainder.

Statement2: $(x - 1)$ is a factor of the polynomial $P (x) = 4 x^{3} - 3 x^{2} + 5 x - 6$ .

p (x) = 3 x^{2} - 5 x + 2

P (x + 2) - P (x) = x^{3} + 3 x^{2} + x + 1

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:

(i)

(ii)

(iii)

α, β

p (x) = 3 x^{2} - 2 x - 6

\frac{1}{α} + \frac{1}{β}

Join BYJU'S Learning Program