Question

One root of the quadratic equation (2x-3) (x+5)=0 is -5, then the other root is​

Answer 1

Step-by-step explanation:

2 roots :

Alpha = -5 , Beta

(2x-3) (x+5) = 0

2x²+10x-3x-15 = 0

2x²+7x-15 = 0

Therefore, a = 2, b = 7, c = -15

We know that,

Alpha * Beta = c/a

-5 * Beta = -15/2

Beta = -15/2*-5

Beta = -15/-10 i.e Beta = 15/10

Therefore, Beta = 1.5 or 3/2

Answer 2

The other root is 1.5

Given :

• The quadratic equation is, (2x-3) (x+5)=0
• One root is -5

To find : The other root.

Solution :

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to calculate the other root of the given quadratic equation)

Let, the other root = y

Product of two roots = (-5) × y = -5y (i)

Now,

(2x-3) (x+5) = 0

or, 2x²-3x+10x-15 = 0

or, 2x²+7x-15 = 0

So, the quadratic equation is :

2x²+7x-15 = 0

Comparing with, ax²+bx+c = 0, we get :

• a = 2
• b = 7
• c = -15

We know that,

Product of two roots = c ÷ a

By, putting the available values, we get :

Product of two roots = (-15) ÷ 2 = -7.5 (ii)

By comparing (i) and (ii), we get :

-5y = -7.5

5y = 7.5

y = 7.5/5

y = 1.5

Hence, the other root is 1.5