What are the roots of the quadratic equation: x
2
+3x−154=0
- A11, 14
- B11, -14
- C14, -11
- D14, -22
Solution & Step-by-step Explanation
Given quadratic equation:
x
2
+3x−154=0
We need to find two numbers that multiply to −154 and add up to 3. These numbers are 14 and −11.
Splitting the middle term:
x
2
+14x−11x−154=0
x(x+14)−11(x+14)=0
(x−11)(x+14)=0
Equating each factor to zero:
x−11=0⟹x=11
x+14=0⟹x=−14
Thus, the roots are 11 and −14.
x
2
+3x−154=0
We need to find two numbers that multiply to −154 and add up to 3. These numbers are 14 and −11.
Splitting the middle term:
x
2
+14x−11x−154=0
x(x+14)−11(x+14)=0
(x−11)(x+14)=0
Equating each factor to zero:
x−11=0⟹x=11
x+14=0⟹x=−14
Thus, the roots are 11 and −14.