Question

If axsquare-7x+c has 14 as the sum of the zeroes and also as the product of the zeroes find the value of a and c

Answer 1

Answer:

a = ½

c = 7

Step-by-step explanation:

Given a quadratic equation such that,

ax^2 - 7x + c = 0

Also, it's given that,

Sum of zeroes = 14

Product of zeroes = 14

Now, we know that,

General form of quadratic equation is,

Ax^2 + Bx + C = 0

On Comparing, we have,

• A = a
• B = -7
• C = c

Also, we know that,

Sum of zeroes = -B/A

=> -(-7)/a = 14

=> 7/a = 14

=> a = 7/14

=> a = 1/2

And, we know that,

Product of zeroes = C/A

=> c/a = 14

=> c = 14a

=> c = 14 × 1/2

=> c = 14/2

=> c = 7

Hence, the required value of a = ½ and c = 7.

Answer 2

Given: An equation ax² - 7x + c, having 14 as the sum and product of its zeros.

To find: The value of a and c.

Answer:

We know that the general form of an equation is ax² + bx + c, where,

• The sum of its zeros is -b/a.
• The product of its zeros is c/a.

Therefore, from the given equation,

• a = a
• b = -7
• c = c

Now, let's solve the sum of its zeros.

As mentioned earlier, the sum is given by -b/a.

$\tt \dfrac{-b}{a}\ =\ \dfrac{7}{a}\\\\\\14\ =\ \dfrac{7}{a}\\\\\\\bf a\ =\ \dfrac{1}{2}$

Again, the product of its zeros is c/a.

$\tt \dfrac{c}{a}\ =\ \dfrac{c}{a}\\\\\\14\ =\ \dfrac{c}{\frac{1}{2}}\\\\\\\dfrac{14}{2}\ =\ c\\\\\\\bf c\ =\ 7$

Therefore, a = 1/2 and c = 7.