The quadratic polynomial whose sum of zeroes is $3$ and product of zeroes is $- 2$ is:

x^{2} + 3 x - 2 = 0

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x^{2} - 2 x + 3 = 0

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x^{2} - 3 x + 2 = 0

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x^{2} - 3 x - 2 = 0

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Solution

The correct option is D $x^{2} - 3 x - 2 = 0$
Given: sum of zeroes is $3$ and product of zeroes is $- 2$
Let the zeroes of the polynomial be $α, β$
According to the question,
$α + β = 3, α β = - 2$
We know, $α + β = - \frac{b}{a} = 3 ⟹ b = - 3 a$ ....... $(i)$
And, $α β = \frac{c}{a} = - 2 ⟹ c = - 2 a$ ....... $(i i)$
Now, the general form of quadratic equation is:
$a x^{2} + b x + c = 0$
From equation $(i)$ and $(i i),$ we get
$a x^{2} + (- 3 a) x + (- 2 a) = 0 ⟹ a (x^{2} - 3 x - 2) = 0$
Hence, the required polynomial is $x^{2} - 3 x - 2 = 0$

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The quadratic polynomial whose sum of zeroes is 3 and product of zeroes is −2 is:

The quadratic polynomial whose sum of zeroes is $3$ and product of zeroes is $- 2$ is: