Question

7. Find the quadratic equation in which the
sum and product of roots are 5 and -6.​

Answer 1

Answer:

The Quadratic equation having Sum of roots = 5 and Product of zeroes = (-6) is x² - 5x - 6.

Step-by-step explanation:

We have,

Sum = 5

Product = (-6)

Let the zeroes be 'a' and 'b'

Then,

a + b = 5

ab = (-6)

Now, we know that, required Quadratic equation is

x² - (a + b)x + (ab)

x² - (5)x + (-6)

x² - 5x - 6

OR

Let the required Quadratic equation be,

ax² + bx + c = 0

To make the coefficient of x² equal to 1, divide the whole equation by a.

So,

(ax²/a) + (bx/a) + (c/a) = 0/a

x² + (b/a)x + (c/a) = 0

Now, we know that,

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

Product of zeroes = (c/a) = (-6)

Now, we can modify the above equation,

x² + (b/a)x + (c/a) = 0

x² - (-b/a)x + (c/a) = 0

Thus,

Putting in the values, we get,

x² - 5x - 6

Hence,

The Quadratic equation having Sum of roots = 5 and Product of zeroes = (-6) is x² - 5x - 6.

Hope it helped and believing you understood it........All the best