Question

using factorization method, find the square roots of the quadratic equation. 3p (2p-1) - 17 = (2p-5)(square)​

Answer 1

Answer:

p = - 2, p = - $\frac{21}{2}$

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 = - $\frac{21}{2}$

Answer 2

Answer:

=>6p² - 3p - 17 = 4p²+ 25 - 20p

=> √2p² + 17p - 42

(to be continued.....)

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