Question

2x2 – 5x + 3 = 0 Which one of the following are the factors of the given quadratic equation?​

Answer 1

$\huge\bold{\gray{\sf{Answer:}}}$

Explanation:

It is in the form of a quadratic equation so we simply factorise it and hence find the roots:

Form of a quadratic equation:$\bold{\red{a {x}^{2} + bx + c}}$

Where c is any constant.

How to factorise..??

step1: Multiply the constant term with coefficient of x square.suppose we obtain 'z' after multiplying

step 2:Think of a number whose sum equal to the coefficient of middle term and product makes the 'z'

step 3: now split the middle term by factors of that number which you think.

step 4:At last take common and compare with equal to 0 we obtain the roots .

$\underbrace{2 {x}^{2} - 5x + 3}_6$

Here ,when we multiply with the coefficient of

x² with constant 3 we get 6.

we have to think of a number whose sum makes the coefficient of x say -5 and product makes 6.

6=>3×2

sum=-3-2

$=>2 {x}^{2} - 3x - 2x + 3$

$=>2 {x}^{2} - 2x - 3x + 3$

$=>2x(x - 1) - 3(x - 1 )= 0$

$=>(2x - 3)(x - 1) = 0$

$= > 2x - 3 = 0$

$=>x = \frac{3}{2}$

$=>x - 1 = 0$

$=>x = 1$

$\therefore$ $\bold{The \:factors\: are \:{\red{x=1}} \:and\: {\green{x = \frac{3}{2}}}}$

Answer 2

$\huge\bold{\gray{\sf{Answer:}}}$

Explanation:

It is in the form of a quadratic equation so we simply factorise it and hence find the roots:

Form of a quadratic equation:$\bold{\red{a {x}^{2} + bx + c}}$

Where c is any constant.

How to factorise..??

step1: Multiply the constant term with coefficient of x square.suppose we obtain 'z' after multiplying

step 2:Think of a number whose sum equal to the coefficient of middle term and product makes the 'z'

step 3: now split the middle term by factors of that number which you think.

step 4:At last take common and compare with equal to 0 we obtain the roots .

$\underbrace{2 {x}^{2} - 5x + 3}_6$

Here ,when we multiply with the coefficient of

x² with constant 3 we get 6.

we have to think of a number whose sum makes the coefficient of x say -5 and product makes 6.

6=>3×2

sum=-3-2

$=>2 {x}^{2} - 3x - 2x + 3$

$=>2 {x}^{2} - 2x - 3x + 3$

$=>2x(x - 1) - 3(x - 1 )= 0$

$=>(2x - 3)(x - 1) = 0$

$= > 2x - 3 = 0$

$=>x = \frac{3}{2}$

$=>x - 1 = 0$

$=>x = 1$

$\therefore$ $\bold{The \:factors\: are \:{\red{x=1}} \:and\: {\green{x = \frac{3}{2}}}}$