Question

If the sum and product of the zeroes of the polynomial ax^2
-5x+c is equal to 10 each ,find the value of 'a' and'c'

Answer 1

Hey there!
For a quadratic polynomial, ax²+bx+c ,
Sum of roots = -b/a
Product of roots = c/a

Given, Quadratic polynomial : ax² - 5x + c

Values of coefficients : a = a, b = -5 , c = c

Now,
Given that, Sum of roots = Product of roots.

Sum of roots = -b/a = -(-5)/a = 5/a

Product of roots = c/a

So, 5/a = c/a

Therefore, c =5 .

Also, Given that Sum of roots = Product of roots = 10

Take Sum of roots,

-(-5)/a = 10

5/a = 10

5 =10 a

a = 5/10 = 1/2

So , a = 1/2 , c = 5

Answer 2

Hey!

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Polynomial = ax^2 -5x + c
Sum of zeros = 10
Product of zeros = 10

We need to find 'a' and 'c'

We know,
Sum of zeroes = - b/a
Product of zeroes = c/a

p (x) = ax^2 - 5x + c
Where,
a = a
b = -5
c = 1

Sum of zeroes = - b/a = - (-5) / a = 5/a
Product of zeroes = c/a = 1 / a = 1/a

A.T.Q

Sum and product of the zeroes = 10
That means,

- b / a = c/a
- b = c
5 = c
c = 5


Now,

Sum of zeroes = 10

5 / a = 10
5 = 10a
a = 5/10
a = 1/2

Now, finally we go values of both 'a' and 'c'

a = 1/2
c = 5

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Hope it helps...!!!