Question

Find the discriminant for the following quadratic equations. Also, determine the nature of the roots.

(i) 5x²–6x–2=0
(ii) x²-3√3x+12=0​​

Answer 1

Answer:

Step-by-step explanation:

D= b²-4ac is called discriminant.

The nature of roots depend upon the value of the discriminant D. Since D can be zero, positive or negative.

When D>0

If D= b²-4ac >0, then

x= -b+√D/2a &  -b-√D/2a

So, the quadratic equation has two distinct real roots.

[ SOLUTION IS IN THE ATTACHMENT]

Verification:

5x²-6x-2=0

5{(3+√19)/5)}² - 6 (3+√19)/5 -2=0

5(9+6√19+19/25) - (18+6√19)/5 -2=0

(9+6√19+19)/5 - (18+6√19)/5 -2=0

(9+6√19+19)/5 - (18+6√19)/5 -2=0

(9+6√19+19)/5 - 18-6√19/5 -2=0

(9 - 18+19+6√19-6√19)/5  -2=0

(-9+19)/5 -2=0

(10/5)-2=0

2-2= 0

0= 0

L.H.S = R.H.S

Similarly we can prove that

5{(3-√19)/5)}² - 6 (3-√19)/5 -2= 0

Answer 2

Answer:

sorry mate I am bit busy now

Step-by-step explanation:

i promise that I'll surely thank you 15 answers ...later

sorry sorry.....