Find the roots of the following quadratic equation, if they exist, by

1.	Find the roots of the following quadratic equation, if they exist, by the method of completing the square:x2 + 5 = -6x
Answer» The given Q.E. is x² + 5 = -6x ⇒ x² + 6x = -5 ⇒ (x)² + 2.(x).3 = -5 Now L.H.S. is of the form a² + 2ab where b = 3. Adding b² = 3² on both sides we get x² + 2(x)(3) + 3² = -5 + 3² (x + 3)² = -5 + 9 = 4 ∴ x + 3 = 74 = ± 2 ⇒ x = +2 – 3 or – 2 – 3 \(\therefore\) x= -1 or -5 are the roots of the given Q.E.

Find the roots of the following quadratic equation, if they exist, by the method of completing the square:x2 + 5 = -6x

Answer»

The given Q.E. is x² + 5 = -6x

⇒ x² + 6x = -5

⇒ (x)² + 2.(x).3 = -5

Now L.H.S. is of the form a² + 2ab where b = 3.

Adding b² = 3² on both sides we get

x² + 2(x)(3) + 3² = -5 + 3²

(x + 3)² = -5 + 9 = 4

∴ x + 3 = 74 = ± 2

⇒ x = +2 – 3 or – 2 – 3

\(\therefore\) x= -1 or -5 are the roots of the given Q.E.