Question

. If ‘m’ and ‘n’ are the zeroes of the polynomial ax2 -5x+c find the value of ‘a’ and ‘c’ when m+n=mn=10

Answer 1

The Image shows the whole solution

Answer 2

Answer: The answer is $\dfrac{1}{2}$ and 5.

Step-by-step explanation:  Given that 'm' and 'n' are the zeroes of the quadratic polynomial $ax^2-5x+c$.

We are to find the value of 'a' and 'c' if m + n = mn = 10.

From the given information, we can say that 'm' and 'n' are the roots of the equation  $ax^2-5x+c=0$.

Therefore, we have

$m+n=-\left(-\dfrac{5}{a}\right)\\\\\Rightarrow 10=\dfrac{5}{a}\\\\\Rightarrow a=\dfrac{1}{2},$

and

$mn=\dfrac{c}{a}\\\\\Rightarrow 10=\dfrac{c}{\frac{1}{2}}\\\\\Rightarrow 2c=10\\\\\Rightarrow c=5.$

Thus, the value of a is $\dfrac{1}{2}$ and the value of c is 5.