Question

If a quadratic polynomial f(x) is not factorizable into linear factors, then it has no real zero. (True/False)

Answer 1

SOLUTION :  

When the Quadratic polynomial f(x)  : ax² + bx + c is not factorizable then the curve y = ax² + bx + c does not touch or cut x-axis. The parabola  y = ax² + bx + c open upwards and remains completely above x axis if a > 0 and open downwards and remains completely below x axis, if a < 0 .

Hence, This statement that if quadratic polynomial is not factorizable into linear factor then it has no real zeros is TRUE.  

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Answer 2

When a quadratic polynomial
$f(x) = a {x}^{2} + bx + c$
is not factorizable into linear factors, then the curve
$y = a {x}^{2} + bx + c$
does not touch x-axis.Parabola
$y = a {x}^{2} + bx + c$
opens upwards above the x-axis or opens downwards below the x-axis,where
$a > 0$
or
$a < 0$
Hence,it has no real zeroes.(True)

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