If the polynomials $f (x) = x^{2} + 5 x - p$ and $g (x) = x^{2} - 2 x + 6 p$ have a common factor, then find the common factor.

x + 2

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

x

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

x + 4

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

Either B or C

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

Open in App

Solution

The correct option is B Either B or C
Given,
$f (x) = x^{2} + 5 x - p$
$g (x) = x^{2} - 2 x + 6 p$

Let $x - k$ be the common factor of f(x) and g(x).

Therefore,
$f (k) = 0$ and $g (k) = 0$

$⟹ k^{2} + 5 k - p = 0$ ......(1)

$k^{2} - 2 k + 6 p = 0$ .......(2)

From equation 1 and 2,we get,
$k = p$

Substituting this value in equation 1,
$p^{2} + 5 p - p = 0$

$p^{2} + 4 p = 0$

$p = 0$ or $p = - 4$

Therefore, $x$ or $x + 4$ is a common factor of f(x) and g(x).

Hence, option D is correct.

Suggest Corrections

Similar questions

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

g (x) = x^{2} - 2 x + 6 p

x + a

f (x) = x^{2} + x - 6

g (x) = x^{2} + 3 x - 18

a

x^{2} - 11 x + a

x^{2} - 14 x + 2 a

a =

If x + a is a common factor of expressions $f (x) = x^{2} + p x + q a n d g (x) = x^{2} + m x + n;$ show that : $a = \frac{n - q}{m - p}$

Two distinct polynomial f(x) and g(x) are defined as follows:

$f (x) = x^{2} + a x + 2; g (x) = x^{2} + 2 x + a$

If the equation f (x) = 0 and g(x) = 0 have a common root, then the sum of the roots of the equation f (x) + g(x) = 0 is

Join BYJU'S Learning Program