Question

QUADRATIC EQUATIONS
4.83
if p and q are the roots of the equation x square - px + q = 0, then
(a) p=? And q=? ​

Answer 1

Answer:

q = 0, p ∈ R

Step-by-step explanation:

x² - px + q = 0

Roots are: (p ± √(p² - 4q) ) ÷ 2

Since, roots exist, (p² - 4q) ≥ 0 ..................(1)

Scenario 1:

p = (p + √(p² - 4q) ) ÷ 2 ⇒ 2p = p + √(p² - 4q)..........(2)

q = (p - √(p² - 4q) ) ÷ 2 ⇒ 2q = p - √(p² - 4q)............(3)

Solving eq (2):

p = √(p² - 4q) ⇒ p² = p² - 4q ⇒ -4q = 0 ⇒ q = 0 and p ∈ R.

p cannot be imaginary due to (1).

Note that, this solution is consistent with (3) as well.

Scenario 2:

p = (p - √(p² - 4q) ) ÷ 2

q = (p + √(p² - 4q) ) ÷ 2

You can solve for this scenario, but you'll eventually end up with the same results.