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(i) Find a quadratic polynomial with zeroes -2 and -1/3.
(ii) What is the quadratic polynomial whose sum of the zeroes is -3/2.:and the product
of the zeroes is -1.
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TRY THIS
(i) Find a quadratic polynomial with zeroes -2 and -1/3.
(ii) What is the quadratic polynomial whose sum of the zeroes is -3/2.:and the product
of the zeroes is -1.
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Answer:
Step-by-step explanation:
1. the zeros of the polynomial are -2,-1/3
(x-2)(x-1/3)
x^2-x/3-2x+2/3
3x^2-x-6x+6=0
3x^2-7x+6=0
2. sum of xeros is -3/2
product of zeros is -1
let the polynomial be k(x^2-(sum of zeros)x+product of zeros)
k(x^2-(-3/2)x+(-1))
k(2x^2+3x-2)
2x^2+3x-2 is our required polynomia;
i) Given:
To find:
Solution:
Let the zeroes be a and b
Required polynomial =
Putting values
k is constant value here
Hence, the Required polynomial is
Another method is by making factors
so,
x = -2 and x = -1/3
[x-(-2) ] and [x-(-1/3)]
=> (x+2) and (x+1/3)
__________________________
ii) Given:
To find:
Solution:
We know that
Polynomial is given by
K is just any constant
So,
The required polynomial =
Hence, the Required polynomial is