8 times of a number is added to its square give a result – 15. Then

1.	8 times of a number is added to its square give a result – 15. Then find the number by using its quadratic equation.
Answer» Let us consider the given number = x Then its square = x² 8 times of it = 8x Now adding the above two x² + 8x result is = – 15 x² + 8x = -15 x² + 8x + 15 = 0 x² + 5x + 3x + 15 = 0 ⇒ x(x + 5) + 3(x + 5) = 0 ⇒ (x + 3) (x + 5) = 0 ∴ x + 3 = 0 or x + 5 = 0 Then x = – 3 or – 5

8 times of a number is added to its square give a result – 15. Then find the number by using its quadratic equation.

Answer»

Let us consider the given number = x Then its square = x²

8 times of it = 8x

Now adding the above two x² + 8x result is = – 15

x² + 8x = -15

x² + 8x + 15 = 0

x² + 5x + 3x + 15 = 0

⇒ x(x + 5) + 3(x + 5) = 0

⇒ (x + 3) (x + 5) = 0

∴ x + 3 = 0 or x + 5 = 0

Then x = – 3 or – 5