Question

Find the unknowns p and q for the perfect square 64x⁴- 16x³ + px² + qx + 1​

Answer 1

Answer:

8:13

The quadratic equation is px² + qx - 6=0

3 Given, x and x = -2 are the roots of

the quadratic equation.

3 Thus, putting x = in equation (i) we get,

2 P(²) 3 +qx 6 0

9 3q + 16 4 px 6 0

9p+ 12q - 96 16 = 0

⇒ 9p+12q-96= 0. 3p+4q-320....(ii)

-2 in equation (i), we get Now, putting x = -2

p(-2)2+q(-2)-6=0

4p-2q-60

2p-q-3-0....(iii)

Now, multiplying equation (iii) by 4, we get

⇒8p-4q-12 = 0