using factorization method, find the square roots of the quadratic equation. 3p (2p-1) - 17 = (2p-5)(square)
2 answers:
Answer:
p = - 2, p = -
Step-by-step explanation:
Given
3p(2p - 1) - 17 = (2p - 5)² ← expand factors on both sides
6p² - 3p - 17 = 4p² - 20p + 25 ( subtract 4p² - 20p + 25 from both sides )
2p² + 17p - 42 = 0
Consider the factors of the product of the coefficient of the p² term and the constant term which sum to give the coefficient of the p- term.
product = 2 × - 42 = - 84 and sum = + 17
Factors are + 21 and - 4
Use these factors to split the p- term
2p² - 4p + 21p - 42 = 0 ( factor the first/second and third/fourth terms )
2p(p - 2) + 21(p - 2) = 0 ← factor out (p - 2) from each term
(p - 2)(2p + 21) = 0
Equate each factor to zero and solve for p
p - 2 = 0 ⇒ p = 2
2p + 21 = 0 ⇒ 2p = - 21 ⇒ p = -
You might be interested in
Answer:
The height of building to the nearest foot is h = 36 foot
Step-by-step explanation:
We have given,
Length of ladder leaning against a building, l = 45 foot
Bottom length between ladder and the building , b = 27
Now, we need to find the height of building to the nearest foot.
Let the height of building be h.
Using Pythagoras theorem,
Here, l = 45 , b = 27 and h =?
So,
h² = 45² - 27²
h = √(45² - 27²)
h = 36
The height of building to the nearest foot is h = 36 foot