CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

If  the sum and product of roots of the quadratic equation $$\displaystyle { ax }^{ 2 }-5x+c$$ are both equal to 10, find the value of $$a$$ and $$c$$. 


A
2,3
loader
B
13,5
loader
C
12,5
loader
D
3,5
loader

Solution

The correct option is C $$\displaystyle \frac { 1 }{ 2 } ,5$$
$$\displaystyle { ax }^{ 2 }-5x+c=0$$
Here, $$\displaystyle b=-5$$
Sum of the roots $$\displaystyle =\dfrac { -b }{ a } =\dfrac { -\left( -5 \right)  }{ a } =\dfrac { 5 }{ a } $$
and product of the roots $$\displaystyle =\dfrac { c }{ a } $$
According to the given, we have
$$\displaystyle \dfrac { 5 }{ a } =10\Rightarrow a=\dfrac { 5 }{ 10 } =\dfrac { 1 }{ 2 } $$
and $$\displaystyle \dfrac { c }{ a } =10\Rightarrow c=10.a=10\times \dfrac { 1 }{ 2 } =5$$

$$\displaystyle a=\dfrac { 1 }{ 2 }$$ and $$ c=5$$

Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image