If the sum of the roots of a quadratic equation is −7 and the product of the roots is 12, find the quadratic equation.
- Ax
2
+7x+12=0 - Bx
2
−7x+12=0 - Cx
2
−7x−12=0 - Dx
2
+7x−12=0
Solution & Step-by-step Explanation
A quadratic equation can be framed using the sum and product of its roots with the formula:
x
2
−(Sum of the roots)x+(Product of the roots)=0
Given:
Sum of the roots=−7
Product of the roots=12
Substitute these values into the formula:
x
2
−(−7)x+12=0
x
2
+7x+12=0
x
2
−(Sum of the roots)x+(Product of the roots)=0
Given:
Sum of the roots=−7
Product of the roots=12
Substitute these values into the formula:
x
2
−(−7)x+12=0
x
2
+7x+12=0