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Find the value of p p^2x^2-12x+p+7 one of the zero is 3/2

Sagot :

sqdancefan

Answer:

  p = 2  or  p = -2 4/9

Step-by-step explanation:

We can substitute x=3/2 into the equation and solve for the values of p that make the result be zero.

  p^2(3/2)^2 -12(3/2) +p +7 = 0

  9/4p^2 -18 + p + 7 = 0 . . . . eliminate parentheses

  9p^2 +4p -44 = 0 . . . . . . simplify and multiply by 4

  (9p +22)(p -2) = 0 . . . . . factor

Values of p that make 3/2 be one of the zeros are ...

  p = -22/9, p = 2

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Additional comment

The zero product rule tells you a product will be zero if and only if a factor is zero. Hence the solutions to the quadratic are values of p that make the factors zero.

  9p +22 = 0   ⇒   9p = -22   ⇒   p = -22/9

  p -2 = 0   ⇒   p = 2

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For p=2, the solution 3/2 has multiplicity 2. For p=-22/9, the other zero is x=123/242.

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