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