How do you factor x2+7x+449?

1 Answer
Jun 13, 2016

x2+7x+449=(x+72+214514)(x+72214514)

Explanation:

In x2+7x+449, the discriminant is 7241(449)=49164949=49216249=(4916)(49+16)49=33×6549=214549, though positive, is not the square of a rational number. Hence we cannot factorize it by splitting middle term.

Hence, the way is to find out zeros of quadratic trinomial x2+7x+449. Zeros of ax2+bx+c are given by quadratic formula b±b24ac2a.

So its zeros, which are two conjugate irrational numbers are given by quadratic formula and are

7±2145492 or

7±214572 or

72±214514 i.e. 72214514 and 72+214514

Now, if α and β are zeros of quadratic polynomial, then its factors are (xα)(xβ)

Hence factors of x2+7x+449 are (x+72+214514) and (x+72214514) and

x2+7x+449=(x+72+214514)(x+72214514)