If $x^{2} - 3 x + 2$ is one of the factors of the expression $x^{4} - p x^{2} + q$ , then

p = 4

and

q = 5

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

p = 5

and

q = 4

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

p = - 5

and

q = - 4

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

p = - 4

and

q = - 5

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

Open in App

Solution

The correct option is B $p = 5$ and $q = 4$
Given, $x^{2} - 3 x + 2 = 0$
$(x - 2) (x - 1) = 0$
$x = 2$ and $x = 1$
Hence, $x = 2$ and $x = 1$ are roots of $x^{4} - p x^{2} + q$
Substituting $x = 1$ , we get
$1 - p + q = 0 \to$ (a)
Substituting $x = 2$ , we get
$16 - 4 p + q = 0 \to$ (b)
Subtracting (b) from (a), we get
$(1 - 16) + 3 p = 0$
$3 p = 15$
$p = 5$ ; Substituting in (a), we get
$1 - 5 + q = 0$
$q = 4$

Suggest Corrections

Similar questions

The missing figure in the expression

(5p +...)² = ....+ 40 pq + 16 q² are:

Express 2pq + 4p + 5q + 10 in the factor form.

(x^{2} - 3 x + 2)

x^{4} - {p x}^{2} + q

p^{3} q^{2} - 6 p^{2} q^{5} + p^{4} q^{4} - 8 p q^{6} + 5 p^{3} q

x^{2} - 3 x + 2

x^{4} - p x^{2} + q = 0

Join BYJU'S Learning Program