The polynomials $a x^{3} + 3 x^{2} - 13$ and $2 x^{3} - 5 x + a$ are divided by $x + 2$ if the remainder in each case is the same, find the value of $a$ .

\frac{1}{9}

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

\frac{1}{4}

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

\frac{5}{9}

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

\frac{4}{5}

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

Open in App

Solution

The correct option is A $\frac{5}{9}$
$p (x) = a x^{3} + 3 x^{2} - 13$ and $q (x) = 2 x^{3} - 5 x + a$
When $p (x)$ and $q (x)$ are divided by $x + 2 = 0 \Rightarrow x = - 2$
$p (- 2) = q (- 2) \Rightarrow a (- 2)^{3} + 3 (- 2)^{2} - 13 = 2 (- 2)^{3} - 5 (- 2) + a$
$\Rightarrow - 8 a + 12 - 13 = - 16 + 10 + a$
$\Rightarrow - 9 a = - 5 \Rightarrow a = \frac{5}{9}$

Suggest Corrections

Similar questions

The polynomials $a x^{3} + 3 x^{2} - 3$ and $2 x^{3} - 5 x + a,$ when divided by x - 4 leave the same remainder in each case. Find the value of a.

P (x) = a x^{3} + 3 x^{2} - 13

g (x) = 2 x^{3} - 4 x + a

(x - 3)

a

p (x) = a x^{3} + 3 x - 13

q (x) = 2 x^{3} - 5 x + 1

x + 2

a

If the polynomials $a x^{3} + 3 x^{2}$ - 13 and $2 x^{3}$ - 5x + a, when divided by (x-2), leave the same remainders, find the value of a.

a

a x^{3} + 3 x^{2} - 9

2 x^{3} + 4 x + a

x + 3

Join BYJU'S Learning Program