Question

Write zero of polynomial x2-x-6

Answer 1

GIVEN :-

• A Polynomial p(x) = x² - x - 6

TO FIND :-

• The zeros of p(x) .

SOLUTION :-

◉ p(x) = x² - x - 6

☯ ACCORDING TO QUESTION

➫ x² - x - 6 = 0

By splitting the middle term,

➫ x² - 3x + 2x - 6 = 0

Taking common

➫ x(x - 3) + 2(x - 3) = 0

➫ (x - 3) (x + 2) = 0

➫ x - 3 = 0 , x + 2 = 0

➫ x = 3 , x = -2

Hence the zeros of the p(x) are 3 and (-2).

ADDITIONAL INFORMATION :-

➠Every linear polynomial in one variable has a unique zero, a non - zero constant polynomial has no zero, and every real number is a zero of the zero polynomial.

➠ Factor theorem :- x - a is a factor of the polynomial p(x) , If p(a) = 0. Also, If x - a is a Factor of p(x) , Then p(a) = 0.

Answer 2

CORRECT QUESTION :-

Write the zeros of Polynomial x² - x - 6

GIVEN :-

• A Polynomial p(x) = x² - x - 6

TO FIND :-

• The zeros of Polynomial p(x)

SOLUTION :-

We have,

• p(x) = x² - x - 6

A.T.Q :-

x² - x - 6 = 0

( By splitting the middle term )

x² - 3x + 2x - 6 = 0

⇒ x (x - 3) + 2 (x - 3) = 0

⇒ (x - 3) (x + 2) = 0

⇒ x - 3 = 0 and x + 2 = 0

⇒ x = 3 and x = - 2

Hence, the zeros of the p(x) are 3 and (-2)$.$