Question

if px^2-3px+9 =0 have equle root then find the value of p​

Answer 1

Method :

Let us take a quadratic equation

  ax² + bx + c = 0 ...(i)

For equal roots, we must have the discriminant ( D ) = 0

  i.e., b² - 4ac = 0 ...(ii)

Solution :

The given equation is

  px² - 3px + 9 = 0 ...(iii)

Comparing (i) and (iii), we get

  a = p , b = - 3p , c = 9

Putting these values in (ii), we get

  (- 3p)² - (4 * p * 9) = 0

  or, 9p² - 36p = 0

  or, p² - 4p = 0

  or, p (p - 4) = 0

Either p = 0 or, p - 4 = 0

i.e., p = 0 , 4

But for the equation, we cannot take p = 0 because for p = 0, there will be no quadratic equation.

         Hence, the value of p is 4

Answer 2

Given Equation :- px² - 3px + 9 = 0

Here , a = p , b = - 3p and c = 9

If the roots are equal then ,

b² - 4ac = 0

( - 3p )² - 4 × p × 9 = 0

9p² - 36p = 0

9p ( p - 4 ) = 0

p - 4 = 0

•°• P = 4

•°• The value of p is 4. [ • Required Answer ]