Question

find the zeros of the polynomial p(x)=x²-x-6.by drawing the graph​

Answer 1

EXPLANATION.

Quadratic equation.

⇒ p(x) = x² - x - 6.

As we know that,

Factorizes the equation into middle term splits, we get.

⇒ p(x) = x² - 3x + 2x - 6.

⇒ p(x) = x(x - 3) + 2(x - 3).

⇒ p(x) = (x + 2)(x - 3).

Zeroes of the equation.

⇒ (x + 2)(x - 3) = 0.

⇒ x = -2  and  x = 3.

⇒ y = x² - x - 6.

Put the value of x = -2 in equation, we get.

⇒ y = (-2)² - (-2) - 6.

⇒ y = 4 + 2 - 6.

⇒ y = 6 - 6.

⇒ y = 0.

Their Co-ordinates = (-2,0).

Put the value of x = 3 in equation, we get.

⇒ y = (3)² - (3) - 6.

⇒ y = 9 - 3 - 6.

⇒ y = 9 - 9.

⇒ y = 0.

Their Co-ordinates = (3,0).

Put the value of x = 0 in equation, we get.

⇒ y = (0)² - (0) - 6.

⇒ y = -6.

Their Co-ordinates = (0,-6).