Question

If the square of difference of the zeroes of the quadratic polynomial x^2+px+49 is 144 then the value of ​

Answer 1

Answer:-

Given Polynomial = x² + px + 45.

Square of the Difference between the zeroes = 144

Let the zeroes of the Polynomial be α , β.

⟹ (α - β)² = 144 -- equation (1)

On comparing with standard form of a quadratic equation,

Let,

• a = 1
• b = p
• c = 45.

We know that,

Sum of the zeroes = - b/a

⟹ α + β = - p/1

⟹ α + β = - p -- equation (2)

Product of the zeroes = c/a

⟹ αβ = 45 -- equation (3)

We know that,

(a - b)² = (a + b)² - 4ab

⟹ (α - β)² = (α + β)² - 4αβ

Putting the values from equations (1) , (2) , (3) we get,

⟹ 144 = ( - p)² - 4(45)

⟹ 144 + 180 = p²

⟹ 324 = p²

⟹ √324 = p

⟹ ± 18 = p

Therefore, the value of p is ± 18.

Answer 2

Given : If the square of difference of the zeroes of the quadratic polynomial x² + px + 49 is 144.

　

To find : What is the value of p.

　

We know that :

→ (a + b)² - 4ab = (a - b)²

→ ab = (-p) , ab = 44

　

here,

→ (a + b)² - 4ab = 144

　

Solution :

→ p² - 4 (45) = 144

→ p² = 144 + 180

→ p = √324

→ p = ±18

　

Therefore, the value of p = ±18.