Question

# A quadratic polynomial, whose zeroes are $$-3$$ and $$4$$ is

A
x2x+12
B
x2+x+12
C
x22x26
D
2x2+2x24

Solution

## The correct option is C $$\dfrac{x^2}{2} - \dfrac{x}{2} - 6$$Quadratic equation with $$\alpha$$ and $$\beta$$ as roots can be written as$$x^2 - (\alpha + \beta) + \alpha\beta=0$$Here, $$\alpha = -3$$ and $$\beta = 4$$$$\therefore \alpha + \beta = -3 + 4 = 1$$and $$\alpha - \beta = -3 \times 4 = -12$$$$\therefore$$ The quadratic equation is$$x^2 - (\alpha + \beta)x + \alpha\beta=0$$$$\Rightarrow x^2 - 1x - 12=0$$$$\Rightarrow \dfrac{x^2}{2} - \dfrac{x}{2} - \dfrac{12}{2}=0$$$$\Rightarrow \dfrac{x^2}{2} - \dfrac{x}{2} - 6=0$$Hence the quadratic polynomial is $$\dfrac{x^2}{2} - \dfrac{x}{2} - 6$$Mathematics

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