Question

The zeroes of the quadratic polynomial x² + 99x + 127 are ______.

Options

• Both positive

• Both negative

• One positive and one negative 

• Both equal

Answer 1

The zeroes of the quadratic polynomial x² + 99x + 127 are both negative.

Explanation:

Let given quadratic polynomial be p(x) = x² + 99x + 127

On comparing p(x) with ax² + bx + c, we get

a = 1,

b = 99 

Aand c = 127

We know that,

`x = (-b +- sqrt(b^2 - 4ac))/(2a)`   .....[By quadratic formula]

= `(-99 +- sqrt((99)^2 - 4 xx 1 xx 127))/(2 xx 1)`

= `(-99 +- sqrt(9801 - 508))/2`

= `(-99 +- sqrt(9293))/2`

= `(-99 +- 96.4)/2`

= `(-2.6)/2, (-195.4)/2`

= `- 1.3, -97.7`

Hence, both zeroes of the given quadratic polynomial p(x) are negative.

Alternate Method:

In quadratic polynomical,

If `{:(a > 0, b > 0, c > 0),(a < 0, b < 0, c < 0):}}`

Then both zeroes are negative.

In given polynomial, we see that 

a = 1 > 0,

b = 99 > 0

and c = 124 > 0

The above condition.

So, both zeroes of the given quadratic polynomial are negative.