if α and β are the zeroes of the p[x]=6x2 -7x+2 .then find a quadratic ploynomial whose zeroes are 1/ α and 1/β?
Answers
Answered by
97
EXPLANATION.
α and β are the zeroes of the polynomial.
⇒ p(x) = 6x² - 7x + 2.
As we know that,
Sum of the zeroes of the quadratic expression.
⇒ α + β = - b/a.
⇒ α + β = -(-7)/6 = 7/6.
Products of the zeroes of the quadratic expression.
⇒ αβ = c/a.
⇒ αβ = (2)/6 = 1/3.
To find :
⇒ 1/α + 1/β.
(α + β)/(αβ).
Put the values in the equation, we get.
⇒ (7/6)/(1/3).
⇒ 7/6 x 3/1.
⇒ 7/2.
⇒ 1/α + 1/β = 7/2.
MORE INFORMATION.
Conjugate roots.
(1) = If D < 0.
One roots = α + iβ.
Other roots = α - iβ.
(2) = If D > 0.
One roots = α + √β.
Other roots = α - √β.
Answered by
70
Given :-
6x² - 7x + 2
To Find :-
Quadratic ploynomial whose zeroes are 1/α and 1/β
Solution :-
On comparing the equation with ax² + bx + c we get
a = 6
b = -7
c = 2
Sum of zeroes = -b/a
Sum = -(-7)/6
Sum = 7/6
Product = c/a
Product = 2/6
Product = 1/3
Now
1/α + 1/β
αβ/α + β
(7/6)/(1/3)
7/6 × 3/1
21/6
7/2
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