a and b are the roots of the equation
x² - 6x + 6 = 0
∴ a + b = -B/A = 6 and ab = C/A = 6

Correct Option: C

a and b are the roots of the equation
x² - 6x + 6 = 0
∴ a + b = -B/A = 6 and ab = C/A = 6
We know that,
a² + b² = (a + b)² - 2ab
= (6)² - 2 x 6 = 36 - 12 = 24
∴ 2(a² + b²) = 2 x 24 = 48

As per the given above question , we can say that
Comparing x² - 5x + 6 = 0 with ax² - bx + c = 0 , we get
a = 1, b = - 5, c = 6

Correct Option: C

As per the given above question , we can say that
Comparing x² - 5x + 6 = 0 with ax² - bx + c = 0 , we get
a = 1, b = - 5, c = 6

x2

1

+

1

x +

1

.

1

= 0

α

β

α

β

x2 -		α + β		x +		1		= 0
		αβ				αβ

As per the given above question , we can say that
Let, the roots be α and −α. Then, sum of roots = 0 Also, roots being not equal, discriminant ≠ 0

Correct Option: D

As per the given above question , we can say that
Let, the roots be α and −α. Then, sum of roots = 0 Also, roots being not equal, discriminant ≠ 0

According to question , we have
Given equation is :- 2^2x - 3 × 2^x × 2² + 32 = 0
⇒ 2^2x - 12 × 2^x + 32 = 0
⇒ y² - 12y + 32 = 0, where 2^x = y

Correct Option: D

According to question , we have
Given equation is :- 2^2x - 3 × 2^x × 2² + 32 = 0
⇒ 2^2x - 12 × 2^x + 32 = 0
⇒ y² - 12y + 32 = 0, where 2^x = y
⇒ ( y - 8 ) ( y - 4 ) = 0
⇒ y = 8, y = 4
∴ 2^x = 8 or, 2^x = 4
⇒ 2^x = 2³ or, 2^x = 2²
⇒ x = 3 or, x = 2.
Therefore , the roots of the equation are 3 and 2.

The given equation is 3x² + (2k + 1)x - k - 5 = 0
Compare with ax² + bx + c = 0, we get
a = 3, b = 2k + 1, c = - k - 5

Correct Option: A

The given equation is 3x² + (2k + 1)x - k - 5 = 0
Compare with ax² + bx + c = 0, we get
a = 3, b = 2k + 1, c = - k - 5