Math, asked by soujanya2003, 1 month ago

The roots of the quadratic equation (2X-3) (x+5)
is -5, then the other root is dash

Answers

Answered by muhammadusman60789
1

Answer:

3/2

Step-by-step explanation:

2

 = 2x ^{2}  + 10x - 3x - 15 \\  = 2x(x + 5) - 3(x + 5) \\  = (2x - 3)(x + 5) \\  2x - 3 = 0 \:  \:  \:  \: or \:  \: x + 5 = 0 \\ 2x = 3 \:  \:  \:  \:  \: or  \:  \: x =  - 5 \\ x =  \frac{2}{3}  \:  \:  \: or \:  \: x =  - 5

Answered by Anonymous
20

Question :

Given quadratic equation \tt (2x - 3)(x + 5)

and first root is -5.

Solution :

First of them lets multiply \tt \: (2x - 3) \: with \: (x + 5)

  • Here we go

 \rightarrow\tt(2x - 3) \times (x + 5)

 \rightarrow\tt 2x \times x + 2x \times 5 + ( - 3) \times x + ( - 3) \times 5

 \rightarrow\tt \: 2 {x}^{2}  + 10x - 3x - 15

 \rightarrow\tt \: 2 {x}^{2}  + 7x - 15

Now, we have the quadratic equation

Before moving ahead we will equate the equation with zero

So,

\rightarrow \tt \: 2 {x}^{2}  + 7x - 15 = 0

Let's find out the another root of the equation

 \Rightarrow\tt \: 2 {x}^{2}  + (10 - 3)x - 15 = 0

 \Rightarrow\tt \: (2 {x}^{2}  + 10x) (- 3x - 15) = 0

 \Rightarrow\tt \: 2x( {x}  + 5) \times  - 3 (x  +  5) = 0

 \Rightarrow\tt \: ( 2x   - 3)   (x  +  5) = 0

 \Rightarrow\tt \: (2x - 3) = 0, \:  \: (x + 5) = 0

\Rightarrow \tt \: 2x - 3 = 0 ,\:  \: x + 5 = 0

Transposing -3 and +5 to R.H.S

\Rightarrow \tt \: 2x  =  + 3  ,\:  \: x  =  - 5

Now again Transposing 2 to R.H.S it goes to denominator

 \Rightarrow\tt \: x  =    \frac{2}{3} ,  \:  \: x  =  - 5

 \tt x  =  - 5 already given

Henceforth,

The another root of the equation is \sf\Large\color{#bf73d9}\frac{2}{3}\footnotesize\color{red}★

━━━━━━━━━━━━━━━━━━━━━━━━━━

\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\tt\color{aqua}{●\mid} \underbrace{\color{teal}{Thànk\:Ü}}\color{aqua}{\mid●}\\

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