# 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)

#### 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 + copen 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