Question : If the sum of the roots of a quadratic equation is 1 and the product of the roots is –20, find the quadratic equation.
Option 1: $x^{2}–x–20=0$
Option 2: $x^{2}+x+20=0$
Option 3: $x^{2}+x–20=0$
Option 4: $x^{2}–x+20=0$
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Correct Answer: $x^{2}–x–20=0$
Solution :
Given: The sum of the roots = 1
The product of the roots is = –20
We know that quadratic equation: $x^{2}–(\text{sum of the root})x+(\text{product of the root})=0$
⇒ $x^{2}–(1)x+(–20)=0$
⇒ $x^{2}–x–20=0$
Hence, the correct answer is $x^{2}–x–20=0$.
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