Question

solve the following quadratic equation for x:(1) 5x²-2x-3=0​

Answer 1

Answer:

x=1 means

Step-by-step explanation:

5*(1)(1)-2*1-3=0

5*1-2-3=0

5-2-3=0

3-3=0

0=0

Answer 2

Answer:

Given,

5x² - 2x - 3 = 0

To Find :-

Value of 'x'.

Solution :-

• To solve this there are two Methods.

1. Splitting the middle term
2. Quadratic Formula.

1) Splitting into the middle terms :-

5x² - 2x - 3 = 0

We can write - 2x as "-5x + 3x":-

5x² - 5x + 3x - 3 = 0

5x(x - 1) + 3(x - 1) = 0

(5x + 3)(x - 1) = 0

(5x + 3) = 0 (or) (x - 1) = 0

5x = - 3 (or) x = 1

x = $\sf\dfrac{-3}{5}$ (or) x = 1

$\sf\therefore$ x = $\sf\dfrac{-3}{5}$ , 1.

2) Quadratic Formula Method :-

Formula :-$\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$

Given equation :-

5x² - 2x - 3 = 0

General form of Quadratic Equation :-

ax² + bx + c = 0

By comparing it with general form of Quadratic Equation :-

a = 5

b = -2

c = -3.

According to Quadratic Formula:-

x = $\sf\dfrac{-(-2)\pm\sqrt{(-2)² - 4(5)(-3)}}{2(5)}$

x = $\sf\dfrac{2\pm\sqrt{4 + 60}}{10}$

x = $\sf\dfrac{2\pm\sqrt{64}}{10}$

x = $\sf\dfrac{2\pm8}{10}$

x = $\sf\dfrac{2 + 8}{10}$ (or) $\sf\dfrac{ 2 - 8}{10}$

x = $\sf\dfrac{10}{10}$ (or) $\sf\dfrac{-6}{10}$

x = 1 (or) $\sf\dfrac{-3}{5}$

$\sf\therefore$ x = $\sf\dfrac{-3}{5}$ , 1.