If the sum of the roots of a quadratic equation is 1 and the product of the roots is −20, find the quadratic equation.
- Ax
2
−x−20=0 - Bx+x+20=0
- Cx
2
+x−20=0 - Dx
2
−x+20=0
Solution & Step-by-step Explanation
A quadratic equation can be framed using the formula:
x
2
−(Sum of roots)x+(Product of roots)=0
Given:
Sum of roots=1
Product of roots=−20
Substituting these values into the formula:
x
2
−(1)x+(−20)=0
x
2
−x−20=0
x
2
−(Sum of roots)x+(Product of roots)=0
Given:
Sum of roots=1
Product of roots=−20
Substituting these values into the formula:
x
2
−(1)x+(−20)=0
x
2
−x−20=0