Question

Find the roots of the equation 5x²-6x-2 = 0 by the method of prime factorisation using splitting the middle term.

Class 10th Maths.​

Answer 1

Step-by-step explanation:

5x²-6x-2=0

x²-6/5x-2/5=0

(x)²-2×x×3/5+(3/5)²-(3/5)²-2/5=0

(x-3/5)²-9/25-2/5=0

(x-3/5)²-9/25-10/25=0

(x-3/5)²-19/25=0

(x-3/5)²-(√19/5)²=0. (a²-b²)=(a+b)(a-b)

(x-3/5+√19/5)(x-3/5-√19/5)=0

(x-3+√19/5)(x-3-√19/5)=0

(x-3+√19/5)=0,x=3-√19/5

(x-3-√19/5)=0,x=3+√19/5

I hope it will help you mark me.

Answer 2

.

Step-by-step explanation:

5x

2

−6x−2=0⇒x

2

−

5

6

x−

5

2

=0⇒x

2

−

5

6

x=

5

2

⇒x

2

−2×

5

3

x+(

5

3

)

2

⇒(x−

5

3

)

2

=

25

10

+

25

9

⇒x−

5

3

=±

5

19

⇒x=

5

±

19

+3