Question

prove that the zero of the quadratic polynomail x^2 + 99x + 127 are both negative

Answer 1

here,
α+β=-b/a=-99
and
αβ=c/a=127
so,
the sum of zeroes is negative and product of zeroes is positive.. therefore, the zeroes are both negative.

Answer 2

Product of zeroes of ax2+ bx + c = c/a
Product of the zeroes of x2+ 99x + 127 = 127

Sol:
The product of zeroes is positive. So either 'both zeroes are positive' or 'both zeroes are negative'.
The zeroes are not equal as discriminant of x2+ 99x + 127 = Ö[992 – 4(127)] is not equal to zero.

Also, the sum of the zeroes is –99 (sum of zeroes of ax2+ bx + c = –b/a)

The sum of zeroes is negative and the product of the zeroes is positive.

So we can conclude that 'both the zeroes of the polynomial are negative'.