InterviewSolution
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InterviewSolution
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The zeroes of the quadratic polynomial `x^(2)+99x +127` areA. both positiveB. both negativeC. one positive and one negativeD. both equal |
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Answer» Correct Answer - B Let given quadratic polynomial be `p(x)=x^(2)+99x +127`. On comparing `p(x)` with `ax^(2)+bx +c`, we get `a = 1, b = 99` and `c = 127` We know that, `x = (-b +- sqrt(b^(2)-4ac))/(2a)` [by quadratic formula] `=(-99+-sqrt((99)^(2)-4xx1xx127))/(2xx1)` `= (-99 +- sqrt(9801-508))/(2)` `= (-99 +-sqrt(9293))/(2)=(-99+-96.4)/(2)` `= (-99+96.4)/(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 polynomilal, if `{:(agt 0,bgt 0 " "c gt 0),(" or",),(alt 0,b lt0 " "clt0):}}`, then both zeroes are negative. In given polynomial, we see that `a = 1 gt 0, b = 00 gt 0` and `c = 127 gt 0` which satisfy the above condition. So, both zeroes of the given quadratic polynomial are negative. |
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