LEVEL-2
9. Ifa and are the zeros of the quadratic polynomial p(x) = 4x² – 5x - 1, find the value of
a²B + aB^2
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Step-by-step explanation:
Given :-
a and B are the zeores of the quadratic polynomial p(x) = 4x²-5x-1.
To find :-
Find the value of a²B+aB² ?
Solution :-
Given quadratic polynomial is p(x) = 4x²-5x-1
On comparing with the standard quadratic polynomial ax²+bx+c then
We have ,
a = 4
b = -5
c = -1
Given that
a ,B are the zeores of p(x)
We know that
Sum of the zeroes = -b/a
=> a+B = -(-5)/4
=> a+B = 5/4 ---------------(1)
Product of the zeroes = c/a
=> a×B = -1/4
=> aB = -1/4 ---------------(2)
Now
The value of a²B+aB²
=> aB(a+B)
From (1)&(2)
=> (-1/4)(5/4)
=> (-1×5)/(4×4)
=> -5/16
a²B+aB² = -5/16
Answer :-
The value of a²B+aB² for the given problem is -5/16
Used formulae:-
- The standard quadratic polynomial is ax²+bx+c
- Sum of the zeroes = -b/a
- Product of the zeroes = c/a
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