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Find the value or values of p in the quadratic equation p2 + 13p – 30 = 0. A. p = 15, p = 2 B. p = –10, p = –3 C. p = 10, p = 3 D. p = –15, p = 2

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p^2+13p-30=0


p +15


p -2


(p+15)(p-2)=0


p= -15


p=2

Answer:

The correct option is D.

Step-by-step explanation:

The given quadratic equation is

[tex]p^2+13p-30=0[/tex]

First find two numbers whose sum is 13 and whose product is -30.

The two numbers are 15 and -2.

[tex]p^2+(15-2)p-30=0[/tex]

[tex]p^2+15p-2p-30=0[/tex]

[tex]p(p+15)-2(p+15)=0[/tex]

[tex](p+15)(p-2)=0[/tex]

By using zero product property, equate each factor equal to 0.

[tex]p+15=0[/tex]

[tex]p=-15[/tex]

[tex]p-2=0[/tex]

[tex]p=2[/tex]

Therefore the values of p are -15 and 2. Option D is correct.

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