Question

Pls answer 29,30 and 31...
Pls do properly.....and if you can solve pls do in a paper

Answer 1

Answer:

Hence, proved p = r .

Step-by-step explanation:

SOLUTION :  

Given : ( x - 2 ) and ( x - 1 / 2 are the factors of  px² + 5x + r.

Let f(x)  = px² + 5x + r………….(1)

f(2) = 0 and f(½) = 0  

On putting f(2) = 0 in eq 1

f(x)  = px² + 5x + r

f(2) = p(2)² + 5 × 2 + r

0 = 4p + 10 + r  

4p + r = - 10 ………..(2)

On putting f(1/2) = 0 in eq 1

f(x)  = px² + 5x + r

f(½) = p(1/2)² + 5(1/2) + r  

0 = p/ 4 + 5 /2 + r

0 = ( p + 10 + 4r ) / 4

0 = p + 10 + 4r  

p + 10 + 4r  

p + 4r = - 10 ………(3)

On solving  equation 2 and 3 ,

4p + r = p + 4r

4p - p = 4r - r

3p = 3r

p = r

Hence, proved p = r .

HOPE THIS ANSWER WILL HELP YOU…..