Question

2. If'a' and are the zeroes of a quadratic polynomial x? - 5. + b and
Q - B 1, then the value of 'b' is (1)
a. -6
b. -5
c. 5
d. 6

Answer 1

Correct Question:

If' a' and 'b' are the zeroes of a quadratic polynomial x² - 5x + b and a - b = 1, then value of 'b' is

a. -6

b. -5

c. 5

d. 6

Step-by-step explanation:

If 'a' and 'b' are the zeroes of a quadratic polynomial.

The given quadratic polynomial x² - 5x + b and a - b = 1.

Compare,

ax² - bx + c

Here,

• a = 1
• b = - 5
• c = b

Now, we know that 'a' and 'b' are the zeroes of a quadratic polynomial.

• Product of zeros = c/a
• Product of zeros = b

• a + b = - b/a
• a + b = - (-5/1 )
• a + b = + 5

Given

• a - b = 1

Squaring both the sides, we have:

• ( a - b )² = 1²

• a² + b² - 2ab = 1

• a² + b² + 2ab - 4ab = 1 ( because 2ab - 4ab = - 2 ab )

• ( a + b )² - 4ab = 1

• 5² - 4b = 1. ( because product of zeros i.e, a and b = b )

• 25 - 4b = 1

• 25 - 1 = 4b

• 4b = 24

• b = 24/4

• b = 6

∴ The value of b = 6

Option d.) is correct ✓

____________________________

Answer 2

Answer:

a + b =0

a - b = -6

a + b =0

a - b = -6