12. If a and b are the roots of 5x2 -px +1 = 0 and a - b = 1, then find p.
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Answered by
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a and b are the roots of 5x² - px + 1 = 0
sum of roots = - Coefficient of x/coefficient of x²
a + b = -(-p)/5 = p/5 ----(1)
product of roots = constant/Coefficient of x²
ab = 1/5 ----(2)
now, a - b = 1
squaring both sides,
⇒(a - b)² = 1
⇒(a + b)² - 4ab = 1
From equation (1) and (2),
⇒(P/5)² - 4/5 = 1
⇒p²/25 = 1 + 4/5 = 9/5
⇒p² = 45
⇒p = ±3√5
Hence , p = + 3√5
sum of roots = - Coefficient of x/coefficient of x²
a + b = -(-p)/5 = p/5 ----(1)
product of roots = constant/Coefficient of x²
ab = 1/5 ----(2)
now, a - b = 1
squaring both sides,
⇒(a - b)² = 1
⇒(a + b)² - 4ab = 1
From equation (1) and (2),
⇒(P/5)² - 4/5 = 1
⇒p²/25 = 1 + 4/5 = 9/5
⇒p² = 45
⇒p = ±3√5
Hence , p = + 3√5
Answered by
1
HELLO DEAR,
GIVEN THAT:-
a and b are the roots of the Equation, 5x² - px + 1 = 0
where,
a = 5 , b = -p , c = 1
a*b = 1/5
a + b = -(-p)/5 = p/5
(a - b)² = (a + b)² - 4ab
(1)² = (p/5)² - 4/5
(P/5)² = (5 + 4)/5
(P/5)² = 9/5
P² = 9*5
P = +-3√5
I HOPE ITS HELP YOU DEAR,
THANKS
GIVEN THAT:-
a and b are the roots of the Equation, 5x² - px + 1 = 0
where,
a = 5 , b = -p , c = 1
a*b = 1/5
a + b = -(-p)/5 = p/5
(a - b)² = (a + b)² - 4ab
(1)² = (p/5)² - 4/5
(P/5)² = (5 + 4)/5
(P/5)² = 9/5
P² = 9*5
P = +-3√5
I HOPE ITS HELP YOU DEAR,
THANKS
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