Find a quadratic polynomial such that sum of its zeroes is 3 and one zero is also 3.
Answers
Given data :
Sum of the zeroes of a quadratic polynomial is 3 and one zero is also 3.
To find : Quadratic polynomial
Calculation :
A quadratic polynomial has 2 zeros.
As per the given data, sum of the two zeroes is 3.
Let the zeroes be a, b
Given, one of the zeroes is 3. let a=3,
That is : a + b = 3
3 + b = 3
b = 3 - 3
b = 0
So, the second zero of the polynomial is 0.
With 3,0 as the zeroes, the quadratic polynomial is :
p(x) = x²−(a+b)x+(ab)
= x²-(3+0)x+(3*0)
= x²-3x+0
Therefore, x²-3x is the polynomial p(x) that satisfies the given data.
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Given : a quadratic polynomial such that sum of its zeroes is 3 and one zero is also 3.
To find : quadratic polynomial
Solution:
One root is 3
another root = α
Sum of roots = 3 + α = 3
=> α = 0
Hence roots are 0 & 3
quadratic polynomial = (x - 3)(x - 0)
= x² - 3x
x² - 3x is a quadratic polynomial such that sum of its zeroes is 3 and one zero is also 3.
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