The graph of the polynomial p(x) = $2 x^{2} + 4 x + 3$ has its least value at the point______

(-1, 9)

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

(1, 9)

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

(-1, 1)

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

(0, 3)

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

Open in App

Solution

The correct option is B (-1, 1)

Given polynomial

$p (x) = 2 x^{2} + 4 x + 3$

$p (x)$ attains a minima when $\frac{d p}{d x} = 0$

as $\frac{d p}{d x} = 4 x + 4$ and $\frac{d^{2} p}{d x^{2}} = 4 > 0$

$∵ \frac{d^{2} p}{d x^{2}} > 0$

$∴ i t^{'} s a p o i n t o f m i n i m a$

now, $\frac{d p}{d x} = 0$ given $4 x + 4 = 0 \Rightarrow x = - 1$

so, $p (x)$ attains minima at $x = - 1$ and $p (- 1) = 2 (- 1)^{2} + 4 (- 1) + 3 = 1$

$∴$ point is $= (- 1, 1)$

Suggest Corrections

Similar questions

2 x^{2} + 4 x + 3

p (x) = 2 x^{2} + \frac{1}{4} x + 13

x = - 1

For each pair of polynomials p(x) and q(x) given below find the degree of p(x) + q(x) and p(x)q(x).

(i)

(ii)

(iii)

(iv)

If product of the two zeroes of the polynomial p(x)=2x³++6x²-4x+9 is 3, then find its third zero

p (x) = (k - 2) x^{2} - 4 x + k

Join BYJU'S Learning Program