Find the zeros of quadratic polynomial x2 + x – 2 and verify the

1.	Find the zeros of quadratic polynomial x2 + x – 2 and verify the relationship between zeros and coeffcient.
Answer» Given quadratic polynomial f(x) = x² + x – 2 = x² + 2x – x – 2 = x (x + 2) – 1 (x + 2) = (x – 1) (x + 2) To find zero, f(x) = 0 (x- 1) (x + 2) = 0 x – 1 = 0 or x + 2 = 0 x = 1 or x = -2 Thus 1 and -2 are two zeros of given polynomial Relation between zeros and coefficient Sum of zeros = 1 + (- 2) = – 1 and product of zeros = 1 × (-2) = -2 Comparing given polynomial with ax² + bx + c a = 1, b = 1 and c = -2 Sum of zeros = -b/a = -1/1 = -1 and product of zeros = c/a = --2/1 = -2 Hence, relationship between zeros and coefficient is verified.

Find the zeros of quadratic polynomial x2 + x – 2 and verify the relationship between zeros and coeffcient.

Answer»

Given quadratic polynomial

f(x) = x² + x – 2 = x² + 2x – x – 2

= x (x + 2) – 1 (x + 2) = (x – 1) (x + 2)

To find zero, f(x) = 0

(x- 1) (x + 2) = 0

x – 1 = 0 or x + 2 = 0

x = 1 or x = -2

Thus 1 and -2 are two zeros of given polynomial

Relation between zeros and coefficient

Sum of zeros = 1 + (- 2) = – 1

and product of zeros = 1 × (-2) = -2

Comparing given polynomial with ax² + bx + c

a = 1, b = 1 and c = -2

Sum of zeros = -b/a = -1/1 = -1

and product of zeros = c/a = --2/1 = -2

Hence, relationship between zeros and coefficient is verified.