Question

If x-4 is a factor of x cube -5x square -px+ 24, find the value of p​

Answer 1

GIVEN :–

• x³ - 5x² - px + 24 = 0 have a factor as x - 4 .

TO FIND :–

• Value of 'p' = ?

SOLUTION :–

• x = 4 will satisfy the given equation.

=> (4)³ - 5(4)² - p(2) + 24 = 0

=> 64 - 80 - 2p + 24 = 0

=> 84 - 80 - 2p = 0

=> 4 - 2p = 0

=> 2p = 4

=> p = 4/2

=> p = 2

• Hence , The value of 'p' is 2 .

Answer 2

Given:-

• f(x) = x³-5x²-px+24
• factor of p(x) = x-4

:$\implies$ x-4 = 0

:$\implies$ X = 4

To find:-

• value of p

Solution:-

• to find p put the value of x in the f(x)

:$\implies$ $\sf(4)³-5(4)²-p(4)+24 = 0$

:$\implies$ $\sf 64-80-4p+24 = 0$

:$\implies$ $\sf-16-4p+24 = 0$

:$\implies$ $\sf 8-4p = 0$

:$\implies$ $\sf 8 = 4p$

:$\implies$ $\sf p = \dfrac{8}{4}$

:$\implies$ $\sf p = 2$

hence 2 is the required answer