Advertisements
Advertisements
प्रश्न
Factorize each of the following quadratic polynomials by using the method of completing the square:
y2 − 7y + 12
उत्तर
\[y^2 - 7y + 12\]
\[ = y^2 - 7y + \left( \frac{7}{2} \right)^2 - \left( \frac{7}{2} \right)^2 + 12 [\text{ Adding and subtracting }\left( \frac{7}{2} \right)^2 ]\]
\[ = (y - \frac{7}{2} )^2 - \frac{49}{4} + \frac{48}{4} [\text{ Completing the square }]\]
\[ = (y - \frac{7}{2} )^2 - \frac{1}{4} \]
\[ = (y - \frac{7}{2} )^2 - \left( \frac{1}{2} \right)^2 \]
\[ = [(y - \frac{7}{2}) - \frac{1}{2}][(y - \frac{7}{2}) + \frac{1}{2}]\]
\[ = (y - \frac{7}{2} - \frac{1}{2})(y - \frac{7}{2} + \frac{1}{2})\]
\[ = (y - 4)(y - 3)\]
APPEARS IN
संबंधित प्रश्न
Factorize each of the following expression:
12m2 − 27
Factorize each of the following expression:
256x5 − 81x
Factorize each of the following expression:
a4b4 − 16c4
Factorize each of the following expression:
49(a − b)2 − 25(a + b)2
Factorize each of the following expression:
x − y − x2 + y2
Factorize each of the following expression:
4(xy + 1)2 − 9(x − 1)2
Factorize each of the following expression:
a4 − 16(b − c)4
Factorize each of the following expression:
x3 − x
Obtain the factors of z2 – 4z – 12.
