Question

which of the following has two equal roots
x square - 2 x minus 1
x square - 2 X + 1
2 x square - 2 X + 1
x square - 2 x minus 3 is equal to zero​

Answer 1

Answer:

x²-2x+1

Explanation:

Compare x²-2x+1 with ax²+bx+c we get,

a = 1 , b = -2 , c = 1

Discreminant (D) = b²-4ac

=(- 2)²-4×1×1

= 4 - 4

= 0

D = 0

Therefore,

x²-2x+1=0 has real and equal roots

••••

Answer 2

ANSWER

Given>

The quadratic polynomials are =>

1) x^2 - 2x - 1 =0

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

3)2x^2 - 2x +1 =0

4)x^2 - 2x - 3 =0

Now to find if they had equal roots we will need to see the value of their discriminant.

If discriminant, d = 0

Then the equation will have real and equal roots.

1)x^2 - 2x - 1 =0

=>d= (- 2)^2 - 4×(1)×(-1)

=>d = 4 + 4

=>d = 8

Since d>0, hence roots will be real and distinct not equal.

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

=>d = (- 2)^2 - 4 ×(1)×(1)

=>d = 4 - 4

=>d =0

Since d=0 hence the equation will have real and distinct roots.

3)2x^2 - 2x +1 =0

=> d= (2)^2 - 4×2×1

=> d = 4 - 8

=> d=0

Since d >0 hence the equation will have real and distinct roots but not equal.

4)x^2 - 2x - 3 =0

=>d = (- 2)^2 - 4×(1)×(-3)

=> d= 4 + 12

=>d = 16

Since d>0 hence the roots will be real and distinct but not equal.

Hence only (2) number has real and equal roots.