Question

solve
the
equation : 2x^2+√15ix-i=0​

Answer 1

Step-by-step explanation:

Solve the following quadratic equations:

Answer

Given

Recall that the roots of quadratic equation ax2 + bx + c = 0, where a ≠ 0, are given by

Here, a = 2,

and c = –i

By substituting i2 = –1 in the above equation, we get

By substituting –1 = i2 in the above equation, we get

We can write 15 – 8i = 16 – 1 – 8i

⇒ 15 – 8i = 16 + (–1) – 8i

⇒ 15 – 8i = 16 + i2 – 8i [∵ i2 = –1]

⇒ 15 – 8i = 42 + (i)2 – 2(4)(i)

⇒ 15 – 8i = (4 – i)2 [∵ (a – b)2 = a2 – b2 + 2ab]

By using the result 15 – 8i = (4 – i)2, we get

[∵ i2 = –1]

Thus, the roots of the given equation are

and

.