Find the zeroes of the quadratic polynomial x² + 7x + 10, and verify the relationship between the zeroes and the coefficients

Solution:

The zeroes of the polynomial are the values of x which satisfies the equation and makes the equation equal to zero as whole.

Let us split the middle term to find the factors of the equation x² + 7x + 10

x² + 7x + 10 = x² + 2x + 5x + 10

Taking out the common terms, we get

x(x + 2) + 5 (x + 2)

(x + 2) (x + 5)

Put both the factors equal to zero. 

x + 2 = 0 and x + 5 = 0

x = - 2 and x = - 5

The zeroes of the polynomial x² + 7x + 10 are - 2 and - 5.

A quadratic polynomial in the form of ax² + bx + c = 0 where a ≠ 0, the coefficients can be expressed as sum and product of the zeroes.

The sum of the zeroes is expressed as - b/ a that is coefficient of x / coefficient of x²

(- 2) + (- 5) = - 7 = - (- 7)/ 1 = - b/ a (∵ coefficient of x / coefficient of x² )

The product of the zeroes is expressed as c/ a that is constant term/ coefficient of x²

- 2 × (- 5) = 10 = 10/ 1= c/ a (∵ constant term/ coefficient of x²)

☛ Check: NCERT Solutions for Class 10 Maths Chapter 2

Find the zeroes of the quadratic polynomial x² + 7x + 10, and verify the relationship between the zeroes and the coefficients

Summary:

The zeroes of the polynomial x² + 7x + 10 are - 2 and - 5. The coefficients of the polynomial can be expressed as the sum and the product of the zeroes.

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