Form a quadratic equation whose roots are $-3$ and $4.$
- $\displaystyle { x }^{ 2 }-x-2=0$
- $\displaystyle { x }^{ 2 }-4x+6=0$
- $\displaystyle { x }^{ 2 }-x-12=0$
- $\displaystyle { x }^{ 2 }-x-6=0$
Reveal answer
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C
Correct answer
Explanation
A quadratic equation with roots r1 and r2 is given by x^2 - (r1 + r2)x + (r1 * r2) = 0. Here, r1 = -3, r2 = 4. Sum = 1, Product = -12. Equation: x^2 - x - 12 = 0.
AI explanation
The required quadratic equation is found using the sum and product of roots formula, x^2 - (sum of roots)x + (product of roots) = 0. For the roots -3 and 4, the sum is 1 and the product is -12. Substituting these values gives the equation x^2 - x - 12 = 0.