Question

if x -2 and x-1/2 are the factors of px3 +5x +r show that p =r
Plzz solve the problem ​

Answer 1

Hello Mate,

Here is your answer,

Given:

• Factors of equation f(x) are:

• x = 2

• x = $\frac{1}{2}$

• f(x) = $p {x}^{2} + {5x}+ r$

To find:

• Proof that p = r, if x = 2 and x = 1/2

Solution:

We Know the roots are:

x = 2

x = 1/2

So first substitute (x = 2) in expression f(x) we get,

$p {(2)}^{2} + 5(2) + r = 0 \\ \\ 4p + 10 + r = 0 \: \: \: \: \: .....(1)$

Now substitute x = 1/2 we get,

$p( { \frac{1}{2} })^{2} + 5( \frac{1}{2} ) + r = 0 \\ \\ \frac{p}{4} + \frac{5}{2} + r = 0 \\ \\ lcm = 4 \\ \\ p + 10 + 4r = 0 \: \: \: \: \: .....(2)$

We Know eq(1) = eq(2)

By equating both the equations we get,

$4p + 10 + r = p + 10 + 4r \\ \\ (4p - p) + (10 - 10) + 4r - r = 0 \\ \\ 3p = 3r \\ \\ p = r$

Hence, proved

Hope it helps:)