A quadratic equation, whose zeroes are $-3$ and $4$, is
- $x^2-x+12=0$
- $x^2+x+12=0$
- $\cfrac{x^2}{2}-\cfrac{x}{2}-6=0$
- $2x^2+2x-24=0$
Reveal answer
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C
Correct answer
Explanation
A quadratic equation with roots r1 and r2 is x^2 - (r1+r2)x + (r1*r2) = 0. Here, sum = -3+4 = 1, product = -3*4 = -12. Equation: x^2 - x - 12 = 0. Option C is (1/2)x^2 - (1/2)x - 6 = 0, which is equivalent to (1/2)(x^2 - x - 12) = 0.
AI explanation
A quadratic equation with zeroes alpha and beta is formed by the formula x^2 - (sum of zeroes)x + (product of zeroes) = 0. Substituting the zeroes -3 and 4 gives x^2 - (-3 + 4)x + ((-3)(4)) = 0, which simplifies to x^2 - x - 12 = 0. Dividing the entire equation by 2 yields x^2/2 - x/2 - 6 = 0. The result is x^2/2 - x/2 - 6 = 0.