You visited us 4 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Factor Theorem

If x2-3 x+2 b...

Question

If $x^{2} - 3 x + 2$ be a factor of $x^{4} - p x^{2} + q$ , then $(p, q) =$

(3,4)

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

(4,5)

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

(4,3)

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

(5,4)

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

Open in App

Solution

The correct option is D (5,4)
$x^{2} - 3 x + 2$ be factor of $x^{4} - p x^{2} + q = 0$
Hence $(x^{2} - 3 x + 2) = 0 \Rightarrow (x - 2) (x - 1) = 0 \Rightarrow x = 2, 1,$ putting these values in given equation
So $4 p - q - 16 = 0 . . . . . . . . (i)$
And $p - q - 1 = 0 . . . . . . . (i i)$
Solving (i) and (ii), we get $(p, q) = (5, 4)$

Suggest Corrections

Similar questions

Q. If

x^{2} - 3 x + 2

is a factor of

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

,then

(p, q) =

Q. If

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

is a factor of

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

, then the value of

p

and

q

are

Q. Find the values of p and q such that

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

has a factor

x^{2} - 3 x + 2

Q. If

x^{2} - 3 x + 2

is one of the factors of the expression

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

, then

If bi-quadratic equation $x^{4} - 2 x^{3} + 4 x^{2} + 6 x - 21 = 0$ can also be written as $(x^{2} + p) (x^{2} - 2 x + q) = 0$ . Find the sum of p + q.

Join BYJU'S Learning Program

If x2−3x+2 be a factor of x4−px2+q, then (p,q)=

The correct option is D (5,4)x2−3x+2 be factor of x4−px2+q=0 Hence (x2−3x+2)=0⇒(x−2)(x−1)=0⇒x=2,1, putting these values in given equation So 4p−q−16=0........(i) And p−q−1=0.......(ii) Solving (i) and (ii), we get (p,q)=(5,4)

If $x^{2} - 3 x + 2$ be a factor of $x^{4} - p x^{2} + q$ , then $(p, q) =$