Question

Factorize the following polynomial and verify the relationship between the zeroes and the coefficients of
the polynomial p(x)=x^2+4x-21

Answer 1

Given :

• Polynomial p(x) = x² + 4x - 21

To Find :

• Zeroes of the polynomial &
• Verify the relationship between zeroes and coefficients.

According to the question,

⇒ x² + 4x - 21

⇒ x² + 7x - 3x - 21

⇒ x(x + 7) - 3(x + 7)

⇒ (x - 3) (x + 7)

So, the zeroes are

• x = 3 and - 7

Verify the relationship between your zeroes and coefficients :-

★ Sum of zeroes :-

⇒ α + β = - b/a

⇒ 3 + (-7) = - 4/1

⇒ 3 - 7 = - 4

⇒ - 4 = - 4

★ Product of zeroes :-

⇒ αβ = c/a

⇒ 3 × (-7) = - 21/1

⇒ - 21 = - 21

Hence,verified.

Answer 2

Given :-

p(x) = x² + 4x - 21

To Find :-

Zeroes and verify the relationship between the zeroes and the coefficients of  the polynomial

Solution :-

x² + 4x - 21 = 0

x² + (7x - 3x) - 21 = 0

x² + 7x - 3x - 21 = 0

x(x + 7) - 3(x + 7) = 0

(x + 7)(x - 3) = 0

So, Either

x + 7 = 0

x = 0 - 7

x = -7

Or,

x - 3 = 0

x = 0 + 3

x = 3

Now

Verification

Sum of zeroes = α + β = -b/a

-7 + 3 = -(4)/1

-4 = -4/1

-4 = -4

Product of zeroes = αβ = c/a

-7 × 3 = -21/1

-21 = -21