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Question
The zeroes of the quadratic polynomial x2 + 99x + 127 are ______.
Options
Both positive
Both negative
One positive and one negative
Both equal
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Solution
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.
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