Advertisements
Advertisements
प्रश्न
Factorize each of the following quadratic polynomials by using the method of completing the square:
a2 − 14a − 51
बेरीज
Advertisements
उत्तर
\[a^2 - 14a - 51\]
\[ = a^2 - 14a + \left( \frac{14}{2} \right)^2 - \left( \frac{14}{2} \right)^2 - 51 [\text{ Adding and subtracting }\left( \frac{14}{2} \right)^2 ,\text{ that is }, 7^2 ]\]
\[ = a^2 - 14a + 7^2 - 7^2 - 51\]
\[ = (a - 7 )^2 - 100 [\text{ Completing the square }]\]
\[ = (a - 7 )^2 - {10}^2 \]
\[ = [(a - 7) - 10][(a - 7) + 10]\]
\[ = (a - 7 - 10)(a - 7 + 10)\]
\[ = (a - 17)(a + 3)\]
\[ = a^2 - 14a + \left( \frac{14}{2} \right)^2 - \left( \frac{14}{2} \right)^2 - 51 [\text{ Adding and subtracting }\left( \frac{14}{2} \right)^2 ,\text{ that is }, 7^2 ]\]
\[ = a^2 - 14a + 7^2 - 7^2 - 51\]
\[ = (a - 7 )^2 - 100 [\text{ Completing the square }]\]
\[ = (a - 7 )^2 - {10}^2 \]
\[ = [(a - 7) - 10][(a - 7) + 10]\]
\[ = (a - 7 - 10)(a - 7 + 10)\]
\[ = (a - 17)(a + 3)\]
shaalaa.com
या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
APPEARS IN
संबंधित प्रश्न
Factorize each of the following expression:
16x2 − 25y2
Factorize each of the following expression:
27x2 − 12y2
Factorize each of the following expression:
36l2 − (m + n)2
Factorize each of the following expression:
25x4y4 − 1
Factorize each of the following expression:
a4 − (2b + c)4
Factorize each of the following expression:
3x3y − 243xy3
Factorize each of the following expression:
x4 − 1
Factorize each of the following expression:
a2 − b2 + a − b
Factorize each of the following expression:
xy9 − yx9
Factorize each of the following expression:
x3 − x
