Question

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.
(I) 1/4,-1​
(II) √2,1/3

Answer 1

Answer:

i)α+β=¼, αβ=(-1)

Quadratic polynomial

=x²-(α+β)x+αβ

=x²-(¼)x+(-1)

=x²-x/4-1

Multiply each term by 4

=x²×4-x/4×4-1×4

=4x²-x-4

ii)α+β=√2, αβ=⅓

Quadratic polynomial

=x²-(α+β)x+αβ

=x²-√2x+⅓

Multiply each term by 3

=x²×3-√2×3x+⅓×3

=3x²-3√2x+1

Answer 2

Step-by-step explanation:

1/4,-1

(II) √2,1/3

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