Question

If p&q are the zeroes of the polynomial f(x)=6Xsquare+X-2 ,find the value of (q/p)+(p/q)

Answer 1

Hi !

f(x) = 6x² + x - 2

p and q are zeros of f(x)

sum of zeros = p + q = -b/a
= -1/6
product of zeros = pq = c/a
= -2/6 = -1/3

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to find
q/p + p/q

cross multiply ,


$\frac{p ^{2} + q^{2} }{pq} = \frac{(p+q) ^{2} - 2pq }{pq} \\ = \frac{(-1/6) ^{2} - 2 * -1/3 }{-1/3}$

= $\frac{ \frac{1}{36} + \frac{2}{3} }{-1/3}$
= [1/36 + 24 / 36] / [ -1/3 ]
= [25/36] / [-1/3]
= 25/36 x -3/1
= 25/-12
= -25/12

therefore ,
(q/p)+(p/q) = -25/12