Question

find value of p and r if x - 2 and x- 1/2 are the factors of px²+5x+r

Answer 1

Answer:

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Step-by-step explanation:

Let f(x) =  px²+5x+r

[ Using factor theorem f (2 and 1/2) = 0]

f(x) = px² + 5x + r

f(2) = p * 2 ² + 5 * 2 + r

0 = 4 P + 10 + r

-10 - 4p = r

Now, to the second factor.

f (1/2) = [1/2]² * p + 5 * 1/2 + r

0 = p/ 4 + 5/2 + r

0 = p + 10 + 4r / 4

[ Now we will substitute the value of r]

0 = p + 10 -40 - 4p  

0 = -3p - 30

30 = -3p

p = -10

And so r = -10 - 10 = -20