Question

find the roots of the quadratic equation 15a^2x^2-16abx-15b^2=0

Answer 1

the roots of the quadratic equation are 5a/3b
and -3a/5b

Answer 2

Given,

The quadratic equation, 15a²x²-16abx-15b² = 0

To find,

The roots of the given quadratic equation.

Solution,

The roots of 15a²x²-16abx-15b² = 0 will be 5b/3a and -3b/5a.

We can easily solve this problem by following the given steps.

According to the question,

15a²x²-16abx-15b² = 0

Now, to find its roots we will use the quadratic formula.

So, we will first find the determinant (D).

D = √b²-4ac

In this quadratic equation, we have a = 15a², b = -16ab, and c = -15b².

D = √(-16ab)²-4(15a²)(-15b²)

D = √256a²b² + 900a²b²

D = √1156a²b²

D = 34ab

Therefore, this equation has two distinct and real roots.

Using the quadratic formula,

x = (-b±√b²-4ac)/2a

x = -(-16ab)±34ab/2(15a²)

x = (16ab±34ab)/30a²

x = 2a(8b±17b)/30a²

x = (8b±17b)/15a

Taking first +,

x = (8b+17b)/15a

x = 25b/15a

x = 5b/3a

Taking -,

x = (8b-17b)/15a

x = -9b/15a

x = -3b/5a

Hence, the roots of 15a²x²-16abx-15b² = 0 are 5b/3a and -3b/5a.