Question

find the zeros of the polymial p(x) =x²+5x+6​

Answer 1

EXPLANATION.

Zeroes of the quadratic polynomial.

⇒ p(x) = x² + 5x + 6.

As we know that,

Factorizes the equation into middle term splits, we get.

⇒ x² + 5x + 6 = 0.

⇒ x² + 3x + 2x + 6 = 0.

⇒ x(x + 3) + 2(x + 3) = 0.

⇒ (x + 2)(x + 3) = 0.

⇒ x = - 2  and  x = - 3.

                                                                                                                     

MORE INFORMATION.

Nature of the roots of the quadratic expression.

(1) = Real and unequal, if b² - 4ac > 0.

(2) = Rational and different, if b² - 4ac is a perfect square.

(3) = Real and equal, if b² - 4ac = 0.

(4) = If D < 0 Roots are imaginary and unequal Or complex conjugate.

Answer 2

Given :

• p ( x ) = x² + 5x + 6

To find :

• Zero of the polynomial .

Solution :

We needed to find zero of the polynomial

So, we need to do p( x ) = 0

Now ,

$\rm \: \red{x²-5x+6=0}$

$\rm \: \blue{x²-3x-2x+6=0}$

$\rm x(x-3)-2(x-3)=0$

$\rm \green{(x-3)(x-2)=0}$

$\rm{x-3=0 \: or \: x-2=0}$

$\rm \green{x=-3 } \: or \: \red{ x=-2}$

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★ The zeroes of the polynomial are x = 3 or x = 2