Question

what is the value of p if x +1/2 is a factor of px² -4px+3

Answer 1

Hey mate !!
Here's your answer ^-^

x=-1/2
p*(-1/2)^2-4*p*(-1/2)+3=0
1/4p+2p+3=0
(1+4p/4)+3=0
5p/4=-3
p=-12/5

Answer 2

Given:

x +1/2 is a factor of px² -4px+3

To Find:

The value of p

Solution:

It is given that x+1/2 is a factor of the quadratic equation px² -4px+3 which means

x = -1/2 will satisfy the equation

So, we will put the value of x in px² -4px+3

px² -4px+3 = 0

p(-1/2)² -4p(-1/2)+3 = 0    [∵ (-1/2)² = 1/4]

p(1/4) + (4p)/2 + 3 = 0

p/4 + 2p +3 = 0               [ Taking 4 as L.C.M]

(p +8p +12)/4 = 0             [ Multiplying both R.H.S and L.H.S by 4]

9p+12 = 0

9p = -12                            [ Dividing both side by 9]

p = -12/9

p = -4/3                            [ Taking 3 as common from both numerator and

                                          denominator]  

Hence, the value of p is (-4/3)