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JUNE megelm.14. Under what condition the polynomiaat condition the polynomial ax+bx+c does not have any real zero. |
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Answer» Roots of Polynomial ax2+ bx+ c = 0Can be calculated by using quadratic equation x=−b±b2−4ac√2aSo we can find out nature of roots by calculate the value of b2- 4ac , As :1 )If b2- 4ac > 0 the quadratic has two real distinct roots2 )If b2-4ac = 0 the quadratic has real and equal roots3 )If b2-4ac < 0 the quadratic has no real roots: they are complexLets have a examplex2+x+ 1Here a = 1 , b = 1 And c = 1Soroots will bex=−1±1−4√2 x=−1±i3√2 ( As we know−1−−−√= i , where i is any imaginary number )So we can see that both roots are not real .SoWe can calculate b2- 4ac = 1 - 4 = -3 < 0So,If the polynomial ax2+bx +c does not have any real zero , than b2- 4ac< 0 . c<0 is the correct answer of the given question c <0 is the correct answer |
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