Question

Can someone help me wirh question c? it deals with quadratic equations and imaginary numbers

Answer 1

Question C:

Concept:

Define Discriminant

The discriminant can be positive, zero, or negative, and this determines how many solutions there are to the given quadratic equation. A positive discriminant indicates that the quadratic has two distinct real number solutions. A discriminant of zero indicates that the quadratic has a repeated real number solution.

The summary of the explanation is given below as

The equation in the question is given below as

`x^2-10x+25=0`

The general form of a quadratic expression is given below as

`ax^2+bx+c=0`

By comparing coefficients, we will have that

`a=1,b=-10,c=25`

Hence,

The Discriminant of the equation will be

`\begin{gathered} D=b^2-4ac \\ D=(-10)^2-4*1*25 \\ D=100-100 \\ D=0 \end{gathered}`

The roots of the equation will be calculated below as

`\begin{gathered} x^2-10x+25=0 \\ two\text{ factors to give a product of 25 and sum of -10} \\ \end{gathered}`
`\begin{gathered} x=(-b\pm√(b^2-4ac))/(2a) \\ x=(-(-10)\pm√(0))/(2*1) \\ x=(10)/(2) \\ x=5 \end{gathered}`

Hence,

The number of roots is 0NE

The nature of the root is REAL