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If a Quadratic Polynomial F(X) is Not Factorizable into Linear Factors, Then It Has No Real Zero. (True/False) - Mathematics

True or False

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

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Solution

When polynomial `f(x)=ax^2 + bx + c` is not factorizable then the curve `y = ax^2 + bx + c` does not touch x-axis. Parabola  `y = ax^2 + bx + c`open upwards above the x-axis or open downwards below x-axis where `a > 0` or `a < 0`

Hence, if quadratic polynomial ` f (x)` is not factorizable into linear factors then it has no real zeros.  True. 

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APPEARS IN

RD Sharma Class 10 Maths
Chapter 2 Polynomials
Q 38 | Page 61
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