Question

Find the zeroes of x2 -2x & verify the relationship between its zeroes & coefficients.

Answer 1

$\huge\bold{\boxed{\rm{\blue{Question}}}}$

Find the Zeroes of x² - 2x - 8 and verify the relationship between its Zeroes and coefficients.

$\sf\large\underline\red{Given\:equation:-}$

x² - 2x - 8

$\sf\large\underline\red{solution:-}$

$\sf{\implies x² - 2x - 8}$

$\sf{\implies x² - 4x + 2x - 8}$

$\sf{\implies x(x - 4) + 2(x - 4)}$

$\sf{\implies (x - 4)(x + 2)}$

The value of x² - 2x - 8 is zero when x - 4 = 0 or x + 2 = 0

i. e, when x = 4 or x = - 2

The zeroes of x² - 2x - 8 are 4 and -2

Sum of zeroes = 4 + (- 2) = 2

Product of Zeroes = - 2 × 4 = - 8

Relationship between the Zeroes and the coefficients for the standard quadratic equation is ax² - bx + c = 0

Sum of roots = - b/a and product of roots= c/a

In the given equation ,

x² - 2x - 8 = 0

where, a = 1 , b = - 2 , c= - 8

Sum of roots = -(- 2/1)= 2

and product of roots = - 8/1 = - 8

Hence, the relationship between the Zeroes and the coefficients is verified.

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