Question

If the sum and product of the zero of the polynomial ax2-5x +c is equal to 10 each find the value of 'a' and 'c'

Answer 1

sum of zeroes = -b/a. = -(-5)/a. =10

then. ,5=10a

a. = 5/10= 1/2

now product of zeroes. =c/a= 10

c/1/2=. 10..............( putting a=1/2 )

now 2c=10

c=10/2

c. = 5

hope it will help you.

Answer 2

Answer:

The value of a is $\frac{1}{2}$ and value of c is 5

Step-by-step explanation:

Explanation:

Given ,  a polynomial $ax^{2} - 5x +c$ whose,

sum  and product of zeroes are equal to 10 each .

Let $\alpha \ and \beta$ be the zeroes of the given polynomial .

Step 1:

As we know that , sum of zeroes of the polynomials is

⇒$\alpha + \beta$ =  $\frac{-coefficient of x }{coefficient of x^{2} }$ =$\frac{-b}{a}$  = $\frac{-(-5)}{a}$  

⇒ $\frac{5}{a}$ = 10                     (Given )

⇒a = $\frac{5}{10} = \frac{1}{2}$

And the product of the  zeroes

⇒$\alpha \beta$ =  $\frac{c}{a}$  ........(i)

Now put the value of a = $\frac{1}{2}$ in (i)  we get

  $\frac{c}{a} = \frac{c}{\frac{1}{2} }$  which is equal to 10 .

⇒2c = 10  ⇒ c = 5

Final answer :

Hence , the value of a is $\frac{1}{2}$ and value of c is 5

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