Question

if both (x-2) and)(x-1/2) are factors of px²+5x+r show that p=r

Answer 1

If (x - 2) and (x - ½) are the factors of px²+5x+r

Thn, px² +5x +r =0.. When, x= 2, ½

Thus,
Putting x =2.. We get,

p(2)² +5×2 +r =0

or, 4p +r +10 =0

or, 4p + r = -10 ___(1)

Now, if we put x = ½, we get,

p(½)² + 5×½ + r = 0

or, p/4 + 5/2 + r =0

or, p + 10 + 4r = 0

or, p +4r = - 10___(2)

Comparing eq (1) & (2)
====================

4p + r = p + 4r

or, 4p - p = 4r - r

or, 3p = 3r

or, p = r ___(proved)

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