Class - 10
Chapter - Polynomials
Q. 16
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Class - 10
Chapter - Polynomials
Q. 16
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Answer only if you know.
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Step-by-step explanation:
Given :-
A quadratic polynomial f(x) = x²-3x-2
α and β are the zeroes of f(x).
To find :-
Find the quardratic polynomial whose zeores are
1/(2α+ β) and 1/(2β+α)?
Solution :-
Given quadratic polynomial f(x) = x²-3x-2
=> f(x) = x²-x-2x-2
=> f(x) = x(x-1)-2(x-1)
=> f(x) = (x-1)(x-2)
To find the zeores of f(x) we write f(x) = 0
=> f(x) = (x-1)(x-2) = 0
=> (x-1) = 0 or (x-2) = 0
=> x = 1 or x=2
So the Zeroes of f(x) are 1 and 2
Let α = 1 and β = 2
Now ,
The value of 1/(2α+ β)
= 1/(2(1)+2)
= 1/(2+2)
= 1/4
and the value of 1/(2β+α)
= 1/(2(2)+1)
= 1/(4+1)
= 1/5
The zeores are 1/4 and 1/5
now,
We know that
The quardratic polynomial whose zeores are α and β is K[x²-(α + β)x+α β]
The Quadratic Polynomial whose zeores are
1 /(2α+ β) and 1/(2β+α)
= K[x²-{(1/4)+(1/5)}x+(1/4)(1/5)]
= K[x²-{(5+4)/20}x+(1/20)]
= K[x²-(9/20)x+(1/20)]
=K[(20x²-9x+1)/20]
If K = 20 then
The required Polynomial is 20x²-9x+1
Answer:-
The required quadratic polynomial whose zeores
are 1 /(2α+ β) and 1/(2β+α) is 20x²-9x+1
Used formulae:-
Verified answer
Answer:
Question 1.
If the sum of zeroes of the quadratic polynomial 3x2 – kx + 6 is 3, then find the value of k. (2012)
Solution:
Here a = 3, b = -k, c = 6
Sum of the zeroes, (α + β) = −ba = 3 …..(given)
⇒ −(−k)3 = 3
⇒ k = 9
Question 2.
If α and β are the zeroes of the polynomial ax2 + bx + c, find the value of α2 + β2. (2013)
Solution:
Important Questions for Class 10 Maths Chapter 2 Polynomials 1