Short Answer Type
9. If a and B are the zeroes of the quadratic
polynomial 3.x2 - 5x – 2, find the value of a2 + B2.
Answers
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Step-by-step explanation:
Given :-
a and B are the zeroes of the quadratic
polynomial 3x² - 5x – 2.
To find :-
Find the value of a² + B²?
Solution :-
Given Quadratic Polynomial is 3x²-5x-2
On Comparing this with the standard quadratic Polynomial ax²+bx+c
We get
a = 3
b = -5
c = -2
Given zeroes of p(x) are a and B
We know that
Sum of the Zeroes = -b/a
=> a + B = -(-5)/3
a + B = 5/3 -----------(1)
Product of the zeroes = c/a
=> a × B = -2/3 --------(2)
We know that
(a+b)² = a²+b²+2ab
=> a²+b² = (a+b)²-2ab
On applying this
a²+B² = (a+B)²-2aB
From (1)&(2)
=> a²+B² = (5/3)²-2(-2/3)
=> a²+B² = (25/9)-(-2×2)/3
=>a²+B² = (25/9)-(-4/3)
=> a²+B² = (25/9)+(4/3)
LCM of 3 and 9 = 9
=> a²+B² = (25+12)/9
=>a²+B² = 37/9
Answer:-
The value of a²+B² for the given problem is 37/9
Used formulae:-
- The standard quadratic polynomial is ax²+bx+c
- Sum of the zeroes = -b/a
- Product of the zeroes = c/a
- (a+b)²=a²+2ab+b²
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