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
Answer:
The correct option is D.
Step-by-step explanation:
The given quadratic equation is
\(p^2+13p-30=0\)
First find two numbers whose sum is 13 and whose product is -30.
The two numbers are 15 and -2.
\(p^2+(15-2)p-30=0\)
\(p^2+15p-2p-30=0\)
\(p(p+15)-2(p+15)=0\)
\((p+15)(p-2)=0\)
By using zero product property, equate each factor equal to 0.
\(p+15=0\)
\(p=-15\)
\(p-2=0\)
\(p=2\)
Therefore the values of p are -15 and 2. Option D is correct.