The equation whose roots are 4 and 5 is
- $ \displaystyle x^{2}+9x+20=0 $
- $ \displaystyle x^{2}-9x-20=0 $
- $ \displaystyle x^{2}-9x+20=0 $
- $ \displaystyle x^{3}+9x+20=0 $
Reveal answer
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C
Correct answer
Explanation
If roots are 4 and 5, the equation is (x-4)(x-5) = x^2 - 9x + 20 = 0.
AI explanation
The required quadratic equation is found by setting the product of (x - root1) and (x - root2) to zero. Substituting the given roots 4 and 5 gives (x - 4)(x - 5) = 0. Multiplying these binomials results in x^2 - 5x - 4x + 20 = 0. Combining like terms yields the equation x^2 - 9x + 20 = 0.