Question

If x2 + x - 1 is a factor of x4 + px? + qx2 - 1, then the values of pand q can be O 2-1 O 1,-2 O 2,1​

Answer 1

Answer:

If x2+x–1 is a factor of x4+px3+qx2–1, then can the values of p and q be (1)2,1(2)1,–2(3)–1,–2(4)–2,–1?

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Let x4+px3+qx2–1=(x2+x–1)(x2+tx+1)(1)

Note that coeff. of x2 and constant have been chosen to suit the product.

x4+px3+qx2–1=x4+(t+1)x3+tx2+(t−1)x–1

Comparing coefficients t−1=0⟹t=1

p=t+1=2

q=t=1

So option (1)2,1 is correct.

Step-by-step explanation:

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