if both (x-2) and (x-1/2) are factorise of px2+5x+r.show that p=r
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Explanation:
Let the polynomial be f(x).
If (x - 2) and (x- 1/2) are factors of f(x), this means that f(2) = f(1/2) =0.
==>
==> ------ i. [∵ f(2) = 0]
==>
==> ------- ii. [∵f(1/2)=0]
When we subtract equation ii. from equation i,
==>
==>
==>
==>
∴
Hence, by substituting the value of p in equation i,
==>
==>
∴
Hence, we have shown that p = r = -2.
Answer: p = r = -2
I hope this helps. :D
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