Math, asked by mthangabalaji6424, 20 days ago

If One root of equation px^2+(√3-√2)x-1=0 is x=1/√3 then find the value of p

Answers

Answered by pg1947945
0

Step-by-step explanation:

  • ⇒  The given quadratic equation is x2+px+q=0 --- ( 1 )
  • ⇒  One root of equation ( 1 ) is 2+3
  • ⇒  If p and q are rational, then unique value of p and q exist.
  • ⇒  If they are not rational, p q may have infinite value as the other root may or may not be irrational.
  • Now, let us assume that p and q are rational numbers.
  • Then, other root of equation ( 1 ) must be 2−3.
  • ⇒  Sum of the roots =−p
  • ⇒  −p=2+3+2−3
  • ⇒  −p=4
  • ∴  p=−4
  • Product of roots =q
  • ⇒  q=(2+3)(2−3)
  • ⇒  q=4−3
  • ⇒  q=1
  • ∴  p=−4 and q=1
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