Question

ᴘʟᴇᴀsᴇ sᴏʟᴠᴇ
a) 6x²-5x+1=0
b) 2x²-5x+3=0​

Answer 1

Answer:

Step-by-step explanation:

6x^2 + 5x - 1 =0

6x^2 - x + 6x - 1 =0

x (6x - 1) +1(6x - 1) =0

(x + 1) (6x - 1) =0

x =-1 , x = 1/6

2

x

2

+

5

x

−

3

=

0

 

2

x

2

+

6

x

−

1

x

−

3

=

0

2

x

(

x

+

3

)

−

1

(

x

+

3

)

=

0

(

2

x

−

1

)

(

x

+

3

)

=

0

Now we can equate the factors with zero to obtain the solutions.

2

x

−

1

=

0

,

x

=

1

2

x

+

3

=

0

,

x

=

−

3

srry idk what hppnd to this format

Answer 2

$\large \sf \underbrace{ \underline{Solution+Explanation}}$

First we have to find roots of equation

➠x²-5x+6

➠x²-2x-3x+6

➠x(x-2)-3(x-2)

➠(x-3)(x-2)

So roots are 3 and 2

which means a=3 and b=2

$\sf We \: have \: to \: find \: equation \: of \: roots \: \frac{a}{2} and \: \frac{b}{2}$

$\sf i.e. \frac{3}{2} \: and \: \frac{2}{2}$

As we know that formula to find quadratic equation using roots is

x²-(sum)x+product

$\sf ➠\:\:x²-(\frac{3}{2}+1)x+(\frac{3}{2}×1)=0$

$\sf➠\:\: x²-(\frac{3+2}{2})x+\frac{3}{2}=0$

$\sf ➠\:\:x²-(\frac{5}{2})x+\frac{3}{2}=0$

$\sf multiply\: this\: equation \:by\: 2$

➠ 2x²-5x+3=0

So this is the required equation.