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
B
13,5
C
12,5
D
3,5

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

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