The equation whose roots are $5, 9$ is
- $\displaystyle { x }^{ 2 }-5x+14=0$
- $\displaystyle { x }^{ 2 }-14x+14=0$
- $\displaystyle { x }^{ 2 }-45x+14=0$
- $\displaystyle { x }^{ 2 }-14x+45=0$
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Correct answer
Explanation
A quadratic equation with roots r1 and r2 is x^2 - (r1+r2)x + (r1*r2) = 0. Here, x^2 - (5+9)x + (5*9) = x^2 - 14x + 45 = 0.
AI explanation
For a quadratic equation with roots alpha and beta, the required equation is given by x^2 - (sum of roots)x + (product of roots) = 0. The sum of the roots 5 and 9 is 14, and their product is 45. Substituting these values gives the equation x^2 - 14x + 45 = 0.