Question

8.
Find the zeroes of the quadratic polynomial P(x) = x2+x-12 and
verify the relationship between the zeroes and the coefficients.​

Answer 1

Given Equation

⇒x² + x - 12 = 0

To Find

⇒Zeroes of Quadratic Polynomial and

⇒verify the relationship between the zeroes and the coefficient

 

Now take

⇒x² + x - 12 = 0

Using Middle term Splitting

⇒x² + 4x - 3x - 12 = 0

⇒x(x + 4) - 3(x + 4) = 0

⇒(x - 3)(x + 4) = 0

⇒x - 3 = 0 and x + 4 = 0

⇒x = 3 and x = -4

We Get

⇒α = 3 and β = -4

Now verify relation

⇒Sum of root ( α + β ) = -b/a

⇒Product of root (αβ) = c/a

Now Put the value on formula

( α + β ) = -b/a

⇒(3 - 4) = -1/1

⇒-1 = -1

(αβ) = c/a

⇒(3×-4) = -12/1

⇒-12 = -12

Hence Proved

Answer 2

✰ Question Given :

• Find the zeroes of the quadratic polynomial P(x) = x² + x - 12 and verify the relationship between the zeroes and the coefficients.

✰ Required Solution :

★ Equation given to us :

• ➼ x² + x - 12

★ By Middle term Splitting :

• ➼ x² + x - 12

• ➼ x² + 4x - 3x - 12

• ➼ (x² + 4x) - ( -3x - 12)

• ➼ x ( x + 4 ) - 3 ( x - 4)

✰ Taking Common :

• ➼ (x - 3 ) ( x + 4)

★ Comparing Both Sides :

• ➼ ax + bx + c = 0

★ Values Calculated :

• ➼ x = +3 ( Alpha) α

• ➼ x = -4 (Beta) β

★ Verifying Relationship :

• ➼ Sum of Zeros = ( α + β) = - b/a

• ➼ Sum of Zeros = (- 4 + 3 ) = - 1

• ➼ - 1 = - 1

• ➼ Products of Zeros = ( α × β) = c / a

• ➼ Products of Zero = ( - 4 × 3 ) = - 12

• ➼ - 12 = - 12

⠀⠀⠀★ Hence Verified ! ★

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