Find a quadratic polynomial, in which the sum and product of zeroes are √2 and -3/2 respectively . Also find zeroes. { Hint : Take x^2-√2x-(3/2) as 1/2 (2x^2-2√2x-3) }.
Answers
your answer is 2x square - 2√2 X -3
Answer:
Step-by-step explanation:
Given, the sum of two zeros are 2.
Product of two zeros is -3/2.
We have to find the quadratic polynomial and its zeros.
A quadratic polynomial in terms of the zeroes (α,β) is given by
x2 - (sum of the zeroes) x + (product of the zeroes)
i.e, f(x) = x2 -(α +β) x +αβ
Here, sum of the roots, α +β = √2
Product of the roots, αβ = 3/2
So, the quadratic polynomial can be written as x² - √2x - 3/2.
The polynomial can be rewritten as (1/2)[2x² - 2√2x - 3].
Let 2x² - 2√2x - 3 = 0
On factoring the polynomial,
2x² + √2x - 3√2x - 3 = 0
√2x(√2x + 1) - 3(√2x + 1) = 0
(√2x - 3)(√2x + 1) = 0
Now, √2x - 3 = 0
√2x = 3
x = 3/√2
Also, √2x + 1 = 0
√2x = -1
x = -1/√2
Therefore, the zeros of the polynomial are -1/√2 and 3/√2
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