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

Question

KollegeApply · Accepted Answer

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.

AChoose Your Answer