Question

Find the condition if the sum of the roots of quadratic equation ax2 – bx – c = 0 is equal to the product of
its roots.

Answer 1

Given,

A quadratic equation ax²-bx-c = 0

To FInd,

The condition if the sum of roots is equal to the product of roots.

Solution,

The given quadratic equation is

ax²-bx-c = 0

The sum of roots  = -b/a

Product of roots = c/a

where b is the coefficient of x, a is the coefficient of x² and c is the constant.

Now, it is given that sum of roots = product of roots

Therefore,

-(-b/a) = -c/a

b = -c

b+c = 0

Hence, the condition, if the sum of the roots is equal to the product of roots, is b+c = 0.

Answer 2

Answer:

The condition is b + c = 0

Step-by-step explanation:

The given quadratic equation is $ax^{2} -bx-c=0$

Compare the given quadratic equation with the standard form $ax^{2} +bx+c=0$

a = a, b = -b, c = -c

The product of the roots is

$\frac{c}{a}=\frac{-c}{a}$ → (1)

The sum of the roots is

$\frac{-b}{a} =\frac{b}{a}$ → (2)

Now, the sum of the roots = the products of the roots

$\frac{b}{a} =\frac{-c}{a}$

b = -c

b + c = 0

Therefore the condition is b + c = 0 for the quadratic equation for which the product of roots is equal to the sum of the roots.