Question

$from \: the \: quadratic \: equation \: whose \: roots \: are \: p + \sqrt{q} and \: p - \sqrt{q}$
​

Answer 1

ᴀɴsᴡᴇʀ

we have, roots or zeroes of the equation equation are;

• p + √q
• p - √q

・sum of zeroes = (p+√q) + (p-√q)

= p + √q + p - √q

= p + p

= 2p .........(i)

・product of zeroes = (p+√q)(p-√q)

= p² - √q²

= p² - q .........(ii)

and we know that, for finding a quadratic polynomial or equation we have to use the formula,

p(x) = k[x² - (sum of zeroes)x + (product of zeroes)]

where, k is constant

→ p(x) = k[ x² - (2p)x + (p²-q)]

→ p(x) = k(x² -2px + p²-q)

• k(x² - 2px - p²-q)

so, the quadratic equation is k(x² - 2px + p²-q) where k is a constant

_____________________

it's in the form of a quadratic equation ax² + bx + c = 0 and a≠0

k(x² -px - p²-q) here,

• a = 1
• b = -2p
• c = p²-q